Mich. Comp. Laws § 404.202

Sec. 2. When such petition is filed, the board of supervisors may, if satisfied that the facts set forth in the petition are true, make and enter into a contract with the institution for the cure of such cases, for the treatment of the same, and the said board of supervisors shall order that the expense for the treatment, not exceeding 100 dollars, be paid out of the county treasury in the manner that other claims and bills against the county are paid.