<PAGE>   1
                       SECURITIES AND EXCHANGE COMMISSION
                              WASHINGTON, DC 20549
                                   FORM 10-Q


                   Quarterly Report Under Section 13 or 15(d)
                     of the Securities Exchange Act of 1934


                        For Quarter Ended March 31, 1998



                                    0-20159
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                            (Commission File Number)


                            CROGHAN BANCSHARES, INC.
 -----------------------------------------------------------------------------
             (Exact name of registrant as specified in its charter)


                    Ohio                                31-1073048
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      (State or other jurisdiction of                (I.R.S. Employer
       incorporation or organization)                Identification No.)


         323 Croghan Street, Fremont, Ohio                   43420
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      (Address of principal executive offices)             (Zip Code)


                                 (419)-332-7301
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              (Registrant's telephone number, including area code)



Indicate by check mark whether the registrant (1) has filed all reports required
to be filed by Section 13 or 15(d) of the Securities Exchange Act of 1934 during
the preceding 12 months (or for such shorter period that the registrant was
required to file such reports), and (2) has been subject to such filing
requirements for the past 90 days. Yes [ X ] No [ ]








          634,526 Common shares were outstanding as of March 31, 1998.




This document contains 11 pages.





<PAGE>   2



                            CROGHAN BANCSHARES, INC.

                                     Index
PART I.                                                               Page(s)

  Item 1.  Financial Statements                                       3 - 6
  Item 2.  Management's Discussion and Analysis                       7 - 9
  Itsm 3.  Quantitative and Qualitative Disclosures About Market
            Risk - There have been no material changes from the 
            information provided in the December 31, 1997 Form 10-K

PART II.

  Item 1.  Legal Proceedings - None
  Item 2.  Changes in Securities - None
  Item 3.  Defaults Upon Senior Securities - None
  Item 4.  Submission of Matters to a Vote - None
  Item 5.  Other Information - None
  Item 6.  Exhibits and Reports on Form 8-K:
             (a)  Exhibit 27 - Financial data schedule                  11
             (b)  None

Signatures                                                              10








<PAGE>   3




<TABLE>
<CAPTION>





                            CROGHAN BANCSHARES, INC.
                     Consolidated Balance Sheets (Unaudited)

                                                                                        March 31           December 31
                    ASSETS                                                                1998                 1997

                                                                                     (Dollars in thousands, except par value)
<S>                                                                                     <C>                  <C>           
CASH AND CASH EQUIVALENTS
  Cash and due from banks                                                               $ 10,374             $  9,735
  Interest-bearing deposits in other banks                                                   -                   -
  Federal funds sold                                                                       8,000                 -
                                                                                        --------             --------
               Total cash and cash equivalents                                            18,374                9,735
                                                                                        --------             --------
INVESTMENT SECURITIES
  Available-for-sale, at market value                                                     36,452               34,197
  Held-to-maturity, at amortized cost, market value of $33,186 in 1998
      and $35,588 in 1997                                                                 33,073               35,467
                                                                                        --------             --------
               Total investment securities                                                69,525               69,664
                                                                                        --------             --------
LOANS                                                                                    232,887              239,076
  Less:  Allowance for possible loan losses                                                3,551                3,518
                                                                                        --------             --------
               Net Loans                                                                 229,336              235,558
                                                                                        --------             --------
BANK PREMISES AND EQUIPMENT, NET                                                           8,098                8,119
ACCRUED INTEREST RECEIVABLE                                                                2,494                2,613
OTHER REAL ESTATE OWNED                                                                       92                  140
INTANGIBLE ASSETS                                                                          8,517                8,672
OTHER ASSETS                                                                                 777                  539
                                                                                       ---------             --------
TOTAL ASSETS                                                                            $337,213             $335,040
                                                                                       =========             ========
     LIABILITIES AND STOCKHOLDERS' EQUITY

LIABILITIES
  Deposits:
     Demand, non-interest bearing                                                       $ 29,821             $ 30,753
     Savings, NOW and Money Market deposits                                              108,531              106,836
     Time                                                                                155,697              151,464
                                                                                        --------             --------
               Total deposits                                                            294,049              289,053

  Federal funds purchased and securities sold under repurchase agreements                  5,876                8,663
  Borrowed funds                                                                           2,475                3,200
  Dividends payable                                                                          285                  285
  Accrued interest, taxes and other expenses                                               2,507                2,249
                                                                                        --------             --------
               Total liabilities                                                         305,192              303,450
                                                                                        --------             --------
STOCKHOLDERS' EQUITY
  Common stock, $12.50 par value.  Authorized 3,000,000 shares; issued and
     outstanding 634,526 shares                                                            7,932                7,932
  Surplus                                                                                  8,989                8,989
  Retained earnings                                                                       15,028               14,587
  Net unrealized holding gain (loss) on securities available-for-sale, net of
     related income taxes                                                                     72                   82
                                                                                        --------             --------
               Total stockholders' equity                                                 32,021               31,590
                                                                                        --------             --------
TOTAL LIABILITIES AND STOCKHOLDERS' EQUITY                                              $337,213             $335,040
                                                                                        ========             ========

</TABLE>

See note to consolidated financial statements.
<PAGE>   4

                            CROGHAN BANCSHARES, INC.
   Consolidated Statements of Operations and Comprehensive Income (Unaudited)
<TABLE>
<CAPTION>


                                                                                                      Three months ended
                                                                                                           March 31
                                                                                                      1998          1997
                                                                                                   (Dollars in thousands,
                                                                                                    except per share data)


<S>                                                                                                  <C>           <C>   
INTEREST INCOME
  Interest and fees on loans                                                                         $5,139        $4,915
  Interest and dividends on investment securities:
     U.S. Treasury securities                                                                           427           489
     Obligations of U.S. Government agencies and corporations                                           376           422
     Obligations of states and political subdivisions                                                   142           166
     Other securities                                                                                    43            54
  Interest on federal funds sold                                                                         76            83
                                                                                                     ------        ------
               Total interest income                                                                  6,203         6,129
                                                                                                     ------        ------
INTEREST EXPENSE
  Interest on deposits                                                                                2,749         2,673
  Interest on other borrowings                                                                          110           138
                                                                                                     ------        ------
               Total interest expense                                                                 2,859         2,811
                                                                                                     ------        ------
               Net interest income                                                                    3,344         3,318

PROVISION FOR LOAN LOSSES                                                                                60            45
                                                                                                     ------        ------
               Net interest income after provision for loan losses                                    3,284         3,273
                                                                                                     ------        ------
NON-INTEREST INCOME
  Trust income                                                                                           87            72
  Service charges on deposit accounts                                                                   168           176
  Gain (loss) on sale of investment securities                                                          -              (6)
  Gain (loss) on sale of loans                                                                           12           -
  Other operating income                                                                                154           140
                                                                                                     ------        ------
               Total non-interest income                                                                421           382
                                                                                                     ------        ------
NON-INTEREST EXPENSES
  Salaries, wages and employee benefits                                                               1,402         1,423
  Net occupancy expense of bank premises                                                                160           164
  Amortization of goodwill and other intangible asset                                                   160           159
  Other operating expenses                                                                              872           844
                                                                                                     ------        ------
               Total non-interest expenses                                                            2,594         2,590
                                                                                                     ------        ------
               Income before federal income taxes                                                     1,111         1,065

FEDERAL INCOME TAXES                                                                                    384           362
                                                                                                     ------        ------
NET INCOME                                                                                           $  727        $  703
                                                                                                     ======        ======

               Net income per share, based on 634,526 shares                                         $ 1.15        $ 1.11
                                                                                                     ======        ======
               Dividends declared, based on 634,526 shares                                           $  .45        $  .45
                                                                                                     ======        ======

COMPREHENSIVE INCOME                                                                                 $  717        $  479
                                                                                                     ======        ======
</TABLE>
See note to consolidated financial statements.
<PAGE>   5
<TABLE>
<CAPTION>

                            CROGHAN BANCSHARES, INC.
                Consolidated Statements of Cash Flows (Unaudited)

                                                                                                      Three months ended
                                                                                                           March 31
                                                                                                      1998          1997
                                                                                                    (Dollars in thousands)
<S>                                                                                                  <C>           <C>   
CASH FLOWS FROM OPERATING ACTIVITIES
  Net income                                                                                         $   727       $  703
  Adjustments to reconcile net income to net cash provided by operating activities:
        Depreciation and amortization                                                                    295          262
        Provision for loan losses                                                                         60           45
        Deferred federal income taxes                                                                    (45)         (33)
        FHLB stock dividend                                                                              (23)         (20)
        Net amortization of investment security premiums and discounts                                     8           20
        Loss (gain) on sale of investment securities                                                     -              6
        Loss (gain) on sale of loans                                                                     (12)         -
        Loss (gain) on sale of equipment                                                                   3          -
        Decrease (increase) in accrued interest receivable                                               119         (111)
        Decrease (increase) in other assets                                                             (190)         (38)
        Increase (decrease) in accrued interest, taxes and other expenses                                309          262
                                                                                                     -------      -------
               Net cash provided by operating activities                                               1,251        1,096
                                                                                                     -------      -------
CASH FLOWS FROM INVESTING ACTIVITIES
  Purchases of investment securities:
        Available-for-sale                                                                            (4,998)      (4,984)
        Held-to-maturity                                                                              (5,361)      (6,070)
  Proceeds from maturities of investment securities                                                   10,515        9,485
  Proceeds from sales of available-for-sale investment securities                                        -            993
  Proceeds from sale of loans                                                                            300          -
  Net decrease (increase) in loans                                                                     5,869        7,943
  Capital expenditures                                                                                  (170)         (26)
  Proceeds from sale of equipment                                                                        -            -
                                                                                                     -------      -------
               Net cash provided by (used in) investing activities                                     6,155        7,341
                                                                                                     -------      -------
CASH FLOWS FROM FINANCING ACTIVITIES
  Net increase (decrease) in total deposits                                                            5,031       (7,051)
  Increase (decrease) in federal funds purchased and securities sold under repurchase agreements      (2,787)      (3,606)
  Repayments of borrowed funds                                                                          (725)        (738)
  Cash dividends paid                                                                                   (286)        (286)
                                                                                                     -------      -------
               Net cash provided by (used in) financing activities                                     1,233      (11,681)
                                                                                                     -------      -------
INCREASE (DECREASE) IN CASH AND CASH EQUIVALENTS                                                       8,639       (3,244)
CASH AND CASH EQUIVALENTS AT BEGINNING OF PERIOD                                                       9,735       16,094
                                                                                                     -------      -------
CASH AND CASH EQUIVALENTS AT END OF PERIOD                                                           $18,374      $12,850
                                                                                                     =======      =======

SUPPLEMENTAL DISCLOSURES 
  Cash paid during the year for:
        Interest                                                                                     $ 2,836      $ 2,918
                                                                                                     =======      =======
        Federal income taxes                                                                         $   -        $   -
                                                                                                     =======      =======
   Transfer of loans to other real estate                                                            $   -        $   -
                                                                                                     =======      =======
</TABLE>

See note to consolidated financial statements.

<PAGE>   6

                            CROGHAN BANCSHARES, INC.
                   Note to Consolidated Financial Statements
                                 March 31, 1998
                                  (Unaudited)


(1)  Consolidated Financial Statements

    The consolidated financial statements have been prepared by Croghan
    Bancshares, Inc. (the "Corporation") without audit. In the opinion of
    management, all adjustments (which include only normal recurring
    adjustments) necessary to present fairly the Corporation's financial
    position, results of operations and changes in cash flows have been made.

    Certain information and footnote disclosures normally included in financial
    statements prepared in accordance with generally accepted accounting
    principles have been omitted. The results of operations for the period ended
    March 31, 1998 are not necessarily indicative of the operating results for
    the full year.











<PAGE>   7



                          CROGHAN BANCSHARES, INC.

                    MANAGEMENT'S DISCUSSION AND ANALYSIS
              OF FINANCIAL CONDITION AND RESULTS OF OPERATIONS

PERFORMANCE SUMMARY

Assets at March 31, 1998 totalled $337,213,000 compared to $335,040,000 at 1997
year end. Total deposits increased to $294,049,000 from $289,053,000 at year end
and total loans decreased to $232,887,000 from $239,076,000 at year end.

Net income for the quarter ended March 31, 1998 was $727,000 or $1.15 per common
share compared to $703,000 or $1.11 per common share for the same period in
1997. Operating results for the quarter ended March 31, 1998 include increases
in the provision for loan losses and interest on deposits (primarily interest on
money market accounts as Croghan implemented a more competitive rate structure
in an effort to maintain the market share of its core deposit base). 

DEPOSITS, LOANS, INVESTMENT SECURITIES, AND STOCKHOLDERS' EQUITY

Total deposits at March 31, 1998 increased $4,996,000 or 1.7 percent from 1997
year end. The liquid deposit category (demand, savings, NOW and money market
deposit accounts) increased $763,000 while the time deposit category increased
$4,233,000. Total loans decreased $6,189,000 or 2.6 percent from 1997 year end.
Total investment securities decreased $139,000 from 1997 year end.

Stockholders' equity at March 31, 1998 increased to $32,021,000 or $50.46 book
value per common share compared to $31,590,000 or $49.79 book value per common
share at December 31, 1997. The balance in stockholders' equity at March 31,
1998 included a net unrealized holding gain on securities classified as
available-for-sale of $72,000 (net of deferred income taxes totalling $37,000).
At December 31, 1997, stockholders' equity included a net unrealized holding
gain on securities classified as available-for-sale of $82,000 (net of deferred
income taxes totalling $42,000). Consistent with the Corporation's quarterly
dividend policy, a dividend of $.45 per share was declared on March 17, 1998 to
be distributed on April 30, 1998.

NET INTEREST INCOME

Net interest income, which represents the excess revenue generated from earning
assets over the interest cost of funding those assets, increased $26,000 for the
quarter ended March 31, 1998 compared to the same period in 1997. The net
interest yield (net interest income divided by average earning assets) was 4.35
percent for the quarters ended March 31, 1998 and 1997.

PROVISION FOR LOAN LOSSES AND THE ALLOWANCE FOR POSSIBLE LOAN LOSSES

The following table details factors relating to the provision and allowance for
the three and twelve month periods:
<TABLE>
<CAPTION>

                                      Three Months Ended    Twelve Months Ended
                                           March 31,            December 31,
                                             1998                  1997
                                                (Dollars in thousands)
<S>                                         <C>                   <C>   
Provision for loan losses charged
  to expense                                 $   60                $  180
Net loan charge-offs                             27                    30
Net loan charge-offs as a percent of
 average outstanding net loans                  .01%                  .01%
Nonaccrual loans                             $  211                $  212
Loans past due 90 days or more                1,307                   582
Potential problem loans, other than those
  past due 90 days or more, nonaccrual,
  or restructured                             2,344                 1,992
</TABLE>
<PAGE>   8
<TABLE>
<CAPTION>
<S>                                           <C>                   <C>
Allowance for possible loan losses            3,551                 3,518
Allowance for possible loan losses as a
  percent of period-end loans                  1.52%                 1.47%
</TABLE>

The first quarter 1998 provision for loan losses appearing in the Consolidated
Statements of Operations and Comprehensive Income totalled $60,000. This
provision compares to $45,000 expensed in the first quarter of 1997. Actual net
loan charge offs were $27,000 for the first three months of 1998 compared to
$5,000 during the same period in 1997.

Nonaccrual loans totalled $211,000 at March 31, 1998 compared to $212,000 at
December 31, 1997. Loans past due 90 days or more increased $725,000 and other
potential problem loans increased $352,000 from the December 31, 1997 figures.
These negative asset quality trends will continue to be monitored throughout
1998 to ensure adequate provisions are calculated and expensed. The
Corporation's allowance for possible loan losses as a percentage of outstanding
loans improved to 1.52 percent at March 31, 1998 compared to 1.47 percent at
December 31, 1997. It is the Corporation's policy to maintain the allowance for
possible loan losses at a level to provide for reasonably foreseeable losses. To
accomplish this objective, a consulting firm conducts a loan review process that
is used to facilitate the early identification of problem loans and to ensure
sound credit decisions. Management considers the allowance at March 31, 1998 to
be adequate to provide for losses inherent to the loan portfolio.

NON-INTEREST INCOME

Total non-interest income increased $39,000 or 10.2 percent for the quarter
ended March 31, 1998 compared to the same period in 1997. Included in non-
interest income for the quarter ended March 31, 1997 were realized losses of
$6,000 on the sale of investment securities that were classified as available-
for-sale. There were no such losses during the same period in 1998.

Trust department fee income increased $15,000 between quarterly periods and
service charges on deposit accounts decreased $8,000 between comparable
quarterly periods. Gains on the sale of loans to the Federal Home Loan Mortgage
Corporation (Freddie Mac) totalled $12,000 in 1998. There were no such gains
during the same period in 1997.

Other operating income increased $14,000 between quarterly periods. Included in
other operating income for the first three months of 1998 were $54,000 in fees
generated from the Specialized Investments Division which markets products that
are not FDIC insured (e.g., mutual funds and annuities). This compares to
$39,000 in fees earned during the same period in 1997.

NON-INTEREST EXPENSES

Total non-interest expenses increased $4,000 for the quarter ended March 31,
1998 compared to the same period in 1997. Salaries, wages and employee benefits
decreased $21,000 between quarterly periods and net occupancy expense of bank
premises decreased $4,000 between quarterly periods.

Goodwill amortization associated with the August 1, 1996 purchase of Union
Bancshares Corp. was basically unchanged for the two comparable quarterly
periods while other operating expenses increased $28,000 or 3.3 percent between
quarterly periods. 

FEDERAL INCOME TAX EXPENSE

Federal income tax expense increased $22,000 or 6.1 percent between quarterly
periods due primarily to improved income before taxes. The Corporation's
effective tax rate for the quarter ended March 31, 1998 increased to 34.6
percent compared to 34.0 percent for the quarter ended March 31, 1997.
<PAGE>   9

LIQUIDITY AND CAPITAL RESOURCES

An average federal funds sold position of $5,789,000 was maintained for the
quarterly period ended March 31, 1998. Short-term borrowings of federal funds
purchased and repurchase agreements averaged $5,318,000 for the quarterly
period. 

Long-term borrowings due to the Federal Home Loan Bank in 1999 totalled
$1,000,000 at March 31, 1998 and throughout the quarterly period ended March 31,
1998. Additionally, borrowings from NBD Bank advanced to fund the 1996 purchase
of Union Bancshares Corp. totalled $1,475,000 at March 31, 1998. The loan is due
on July 31, 1999 and is repayable in quarterly installments of principal plus
interest, with the principal payments based upon a ten-year amortization
schedule.

Capital expenditures for bank premises and equipment totalled $170,000 for the
quarter ended March 31, 1998. This compares to $26,000 for same period in 1997.
Projected 1998 capital expenditures total $550,000. Of the projected 1998
expenditure amount, approximately $200,000 is allocated to the relocation and
furnishing of the Trust Department within the Main Office complex.





<PAGE>   10


                                  SIGNATURES




Pursuant to the requirements of the Securities Exchange Act of 1934, the
registrant has duly caused this report to be signed on its behalf by the
undersigned thereunto duly authorized.



                                               CROGHAN BANCSHARES, INC
                                            -------------------------------
                                                      Registrant



Date:      April 14, 1998                       /s/ Thomas Hite
      ------------------------              -------------------------------
                                               Thomas F. Hite, President



Date:      April 14, 1998                      /s/ Allan E. Mehlow
      ------------------------              -------------------------------
                                               Allan E. Mehlow, Treasurer/
                                               Principal Financial Officer