Mich. Comp. Laws § 801.90

Sec. 10. Consistent with section 7, the county may file the civil action in the district court to recover a money judgment and to enforce that judgment in the same manner as other money judgments entered by the district court. If the defendant is still a prisoner in the county jail, venue in a district of the first class is proper in the county where the county jail is located and in a district of the second or third class is proper in the district where the county jail is located. If the defendant is a prisoner in a state correctional facility, venue is proper in the county in which the state correctional facility is located.