Mich. Comp. Laws § 168.205

Sec. 205. Any person duly elected to any of the county offices named in section 200 of this act who desires to resign shall file a written notice containing the effective date of such resignation with the presiding or senior judge of probate, the county clerk and the prosecuting attorney of said county: Provided, That if the county clerk or the prosecuting attorney desires to resign, he shall file a written notice containing the effective date of such resignation with the presiding judge of that judicial circuit.