Exhibit 32

Certification of Periodic Report

Pursuant to 18 U.S.C. § Section 1350

As adopted pursuant to Section 906 of the Sarbanes-Oxley Act of 2002

Pursuant to, and for purposes only of, 18 U.S.C. § 1350, each of the undersigned hereby certifies that (i) the Quarterly Report of Farmers and Merchants Bancshares, Inc. on Form 10-Q for the quarter ended June 30, 2024 filed with the Securities and Exchange Commission (the “Report”) fully complies with the requirements of Section 13(a) or 15(d) of the Securities Exchange Act of 1934, and (ii) information contained in the Report fairly presents, in all material respects, the financial condition and results of operations of Farmers and Merchants Bancshares, Inc.