Mich. Comp. Laws § 404.205

Sec. 5. Any person who shall be treated at any institute under the provisions of this statute may at any time reimburse the county by paying to the county treasurer the amount thereof, and the treasurer shall give him a receipt for the amount so paid, which receipt shall state that such payment is for reimbursement, as aforesaid, and the amount so paid shall be turned into the general fund.