Mich. Comp. Laws § 331.204
A board of trustees for the management of any hospital created hereunder shall be appointed by the board of supervisors of the county in which such hospital is to be acquired, maintained and operated. Said trustees shall be residents and freeholders of the county and may be members of the board of supervisors. Said board shall consist of 5 members to be appointed for terms of 3 years each: Provided, That of the members first appointed 1 shall be appointed for a term of 3 years, 2 for terms of 2 years each, and 2 for terms of 1 year each. Thereafter, each trustee shall hold office for a period of 3 years beginning on the first day of January next ensuing and until a successor is appointed and qualified. Each such trustee shall file with the county clerk the constitutional oath of office. It shall be the duty of said board of trustees to cooperate and advise with the state health commissioner and with the board of supervisors of the county, or with any committee selected thereby, in the equipping of the hospital. As soon as such hospital or institution is completed and equipped, the management and control thereof shall vest in said board of trustees, subject to the provisions of this act and subject to any direction or resolution of the board of supervisors of the county or any committee of said board of supervisors selected for that purpose.
MCL 331.204