Exhibit 32

Certification Pursuant to 18 U.S.C. Section 1350,

as Adopted Pursuant to

Section 906 of the Sarbanes-Oxley Act of 2002

In connection with the Quarterly Report of Farmers & Merchants Bancorp (the “Company”) on Form 10-Q for the quarterly period ended June 30, 2012 as filed with the Securities and Exchange Commission on the date hereof (the “Report”), we, Kent A. Steinwert, Chairman, President and Chief Executive Officer, and Stephen W. Haley, Executive Vice President and Chief Financial Officer of the Company, certify pursuant to Rule 13a-14(b) or Rule 15d-14(b) under the Securities Exchange act of 1934 and Section 906 of the Sarbanes-Oxley Act of 2002 (18 U.S.C. $ 1350), that:

1. the Report fully complies with the requirements of section 13(a) or 15(d) of the Securities Exchange Act of 1934 (15 U.S.C. $ 78m or 78o(d)); and

2. the information contained in the Report fairly presents, in all material respects, the financial condition and results of operations of the Company.

August 6, 2012

/s/ Kent A. Steinwert

Kent A. Steinwert

Chairman, President

& Chief Executive Officer

/s/ Stephen W. Haley

Stephen W. Haley

Executive Vice President & Chief Financial Officer

A signed original of this written statement required by Section 906 has been provided to the Company and will be retained by the Company and furnished to the Securities and Exchange Commission or its staff upon request.