Mich. Comp. Laws § 400.154

Sec. 4. Not more than 4 members of the county board of commissioners shall be members of the board of county institutions. They shall be entitled, for attending meetings, to per diem compensation and other expenses in the same manner as members of the county board of commissioners. The members of the board of county institutions who are not members of the county board of commissioners shall also be entitled to per diem compensation and other expense for attending meetings the same as members of the board of county institutions who are members of the county board of commissioners. The board shall meet at least once a month. However they may not claim reimbursement for attending more than 36 meetings a year.