<PAGE>

                                                                    Exhibit 31.2

                                 CERTIFICATIONS

I, Barbara J. Britenriker, Chief Financial Officer of Farmers & Merchants
Bancorp, Inc., certify that:

6.  I have reviewed this annual report on Form 10-K of Farmers & Merchants
    Bancorp, Inc.;

7.  Based on my knowledge, this report does not contain any untrue statement
    of a material fact or omit to state a material fact necessary to make the
    statements made, in light of the circumstances under which such statements
    were made, not misleading with respect to the period covered by this
    report;

8.  Based on my knowledge, the financial statements, and other financial
    information included in this report, fairly present in all material respects
    the financial condition, results of operations and cash flows of the
    registrant as of, and for, the periods presented in this report;

9.  The registrant's other certifying officer(s) and I are responsible for
    establishing and maintaining disclosure controls and procedures (as defined
    in Exchange Act Rules 13a-15(e) and 15d-15(e)) and internal control over
    financial reporting (as defined in Exchange Act Rules 13a-15(f) and
    15d-15(f) for the registrant and have:

      (e) Designed such disclosure controls and procedures, or caused such
      disclosure controls and procedures to be designed under our supervision,
      to ensure that material information relating to the registrant, including
      its consolidated subsidiaries, is made known to us by others within those
      entities, particularly during the period in which this report is being
      prepared;

      (f) Designed such internal control over financial reporting, or caused
      such internal control over financial reporting to be designed under our
      supervision, to provide reasonable assurance regarding the reliability of
      financial reporting and the preparation of financial statements for
      external purposes in accordance with generally accepted accounting
      principles;

      (g) Evaluated the effectiveness of the registrant's disclosure controls
      and procedures and presented in this report our conclusions about the
      effectiveness of the disclosure controls and procedures, as of the end of
      the period covered by this report based on such evaluation; and

      (h) Disclosed in this report any change in the registrant's internal
      control over financial reporting that occurred during the registrant's
      most recent fiscal quarter (the registrant's fourth fiscal quarter in the
      case of an annual report) that has materially affected, or is reasonably
      likely to materially affect, the registrant's internal control over
      financial reporting; and

10. The registrant's other certifying officer(s) and I have disclosed, based on
    our most recent evaluation of internal control over financial reporting, to
    the registrant's auditors and the audit committee of the registrant's board
    of directors (or persons performing the equivalent functions):

      (a) All significant deficiencies and material weaknesses in the design or
      operation of internal control over financial reporting which are
      reasonably likely to adversely affect the registrant's ability to record,
      process, summarize and report financial information; and

      (b) Any fraud, whether or not material, that involves management or other
      employees who have a significant role in the registrant's internal control
      over financial reporting.

Date: February 17, 2005                  /s/ Barbara J. Britenriker
                                         ---------------------------------------
                                         Barbara J. Britenriker,
                                         Chief Financial Officer