Exhibit 32.1

CERTIFICATION OF CHIEF EXECUTIVE OFFICER

PEOPLES FINANCIAL CORPORATION

PURSUANT TO 18 U.S.C. ss. 1350

I, Chevis C. Swetman, Chairman, President and Chief Executive Officer of Peoples Financial Corporation (the “Company”), hereby certify that the accompanying report on Form 10-Q for the period ending March 31, 2016 and filed with the Securities and Exchange Commission on the date hereof pursuant to Section 13(a) of the Securities Exchange Act of 1934 (the “Report”) by the Company fully complies with the requirements of that section.

I further certify that the information contained in the Report fairly presents, in all material respects, the financial condition and results of operations of the Company.

By:	/s/ Chevis C. Swetman
	Chevis C. Swetman, Chairman, President and Chief Executive Officer (principal executive officer)
Date:	May 11, 2016