Mich. Comp. Laws § 769.35

Sec. 35. The department of corrections shall operate a jail reimbursement program that provides funding to counties for housing offenders in county jails who otherwise would have been sentenced to prison. The criteria for reimbursement, including but not limited to criteria for determining those offenders who otherwise would have been sentenced to prison, and the rate of reimbursement shall be established in the annual appropriations acts for the department of corrections.