Mich. Comp. Laws § 259.803

Sec. 3. Of the county members first appointed, 1 member shall be appointed for 4 years and 1 member for 3 years. Of the city members, 1 shall be appointed for 2 years, 1 for 3 years and 1 for 4 years. After the initial appointments expire all members shall be appointed for 4 years. All members appointed shall serve until they are reappointed or a successor named at the end of their term. If a member is unable to complete his term of office, a successor shall be appointed in the same manner as the original appointment to complete the term. In the case of the appointment of a successor, he shall serve until another is appointed or he is reappointed.