Mich. Comp. Laws § 45.512

Sec. 12. A vacancy in the office of any commissioner shall be filled by a qualified elector selected by the commission. If the commission fails to fill the vacancy within a period of 7 days, the chairman of the board of supervisors shall fill the vacancy forthwith. The new appointee shall be a qualified elector from the same district as the commissioner vacating the office and from the same party.