Mich. Comp. Laws § 331.153
If a majority of all the votes cast upon the question are in favor of establishing a county public hospital, the board of commissioners shall proceed at once to appoint 9 trustees chosen from the citizens at large of the county with reference to their fitness to such office, 1 of whom shall be the chief executive officer of the hospital and not more than 3 of whom may be licensed physicians, who shall constitute a board of trustees for the public hospital. The trustees shall hold their offices until the end of the next following calendar year. In September, prior to the expiration of their terms of office, the board of trustees shall submit to the board of commissioners the names of not more than 2 qualified candidates for each appointment or reappointment. The board of commissioners, at its October meeting, shall appoint for terms commencing next January 1, 3 trustees for 2 years, 3 trustees for 4 years and 3 trustees for 6 years. As terms expire thereafter appointments shall be made for 6 years in the same manner. Appointments to unexpired terms shall be made in the same manner. All appointments and reappointments shall meet general eligibility qualifications hereinbefore stated.
MCL 331.153