Mich. Comp. Laws § 38.4

Sec. 4. (a) Any vacancy occurring 90 days or more before the expiration of the term of any employee or retirant member of the retirement board shall be filled by appointment by the governor. The person thus appointed shall serve for the balance of the unexpired term. (b) Any employee or retirant member of the retirement board who fails to attend the scheduled meetings of the retirement board for 3 consecutive months or longer, without valid excuse, shall be considered as having resigned from board membership and the retirement board shall declare his office vacated as of the adoption of a proper resolution, and shall notify the governor of the vacancy.