Exhibit 4.1


 


FARMERS AND MERCHANTS BANCSHARES,
INC.


DIVIDEND REINVESTMENT PLAN


 


AUTHORIZATION FORM FOR DIVIDEND
REINVESTMENT






This form is to be used
by an eligible stockholder of Farmers and Merchants Bancshares, Inc. (the “Company”) who desires to (i) enroll in the
Company’s Dividend Reinvestment Plan (the “Plan”), (ii) change his or her level of participation in the Plan,
and (iii) terminate his or her participation in the Plan. The Plan is not available to stockholders of record who reside in Arizona,
California or Ohio, or to any other stockholder who resides in any jurisdiction to whom it is unlawful for the Company to make
offers or sales under the Plan in such jurisdiction. Complete and sign below and return it in the enclosed envelope.


 


This form will authorize
the Company to forward to the administrator of the Plan all or a portion of the dividends paid on your shares of the Company’s
common stock to be invested in additional shares of common stock. All investments are made subject to the terms and conditions
of the Plan as set forth in the prospectus in respect of the Plan. This form is also to be used by a participant who desires to
terminate his or her participation and thereby receive all cash dividends.


 


This authorization is
given by you with the understanding that you may terminate it at any time by so notifying the administrator of the Plan.


 


If you choose partial
dividend reinvestment or you terminate your participation in the Plan and would like to have your dividends deposited automatically
into your checking or savings account, complete the section below for Direct Deposit.


 


Please read carefully. This is not


a proxy. Return this form only
if


you wish to participate in the


Plan.


 


Please enroll me in the Plan


 


		 ̈	Full Dividend Reinvestment. Please apply the dividends on all shares of common stock that I currently own as well as
all future shares that I acquire.



 


		 ̈	Partial Dividend Reinvestment. Please apply the dividends on ___________ shares of common stock that I currently own
(the “Plan Shares”) and remit to me the dividends on all other shares that I own.



I understand that the dividends
on my Plan Shares, as well as all future shares that I acquire under the Plan, will be reinvested under the Plan.


 


		 ̈	Terminate Participation – Receive All Cash (no dividend reinvestment)



 


By signing below, I represent that I have received a copy of
the prospectus, dated June 1, 2017, relating to the Plan, as amended and supplemented to date.


 








	Date:	 	 	Account #:	 	 
	 	 	 	 
	 	 	 	 
	Signature(s): 	 	Print Name(s):	 
	 		 	 
	 	 	 	 
	 	 	 	 
	 	 	 	 










 





All joint owners must sign exactly as names appear
on the stock certificates.


 




     


     


    

 


		 ̈	Direct Deposit (check this box only if you checked “Partial Dividend Reinvestment” or “Terminate Participation
– Receive All Cash” above). I hereby authorize American Stock Transfer & Trust Company, LLC (the “Administrator”)
and Farmers and Merchants Bancshares, Inc. (the “Company”) to initiate cash dividend deposits into my account indicated
below and the financial institution below to deposit the same to such account. This authority is to remain in full force and effect
until the Administrator or the Company has received written notification from me of its termination in such time and manner as
to afford them a reasonable opportunity to act on it. If this option is not selected, your dividend check will be automatically
mailed to your address.



(You must complete this section
and return the form along with a personal voided check to enroll for Direct Deposit of your dividends. Your financial institution
can provide you with the following required information.)


 





	Type of Account:	 ̈ Checking	 ̈
    Savings	 



 









	Financial Institution RT/ABA Number:	 	 
	 	 	 
	Address of Financial Institution:	 	 
	 	 	 
	Checking/Savings Account Number:	 	 















 








	Signatures (All Holders Must Sign)	 	 	 
	 	 	 	 	 
	 	 	 
	 	 	 	 	 
	 	 	 
	(Print Name)	(Date)	 	(Print Name)	(Date)




 


 





	Mail completed form to:	Farmers and Merchants Bancshares, Inc.
	 	4510 Lower Beckleysville, Rd, Suite H
	 	Hampstead, MD 21074
	 	Attn: Lynnette Kitzmiller