Mich. Comp. Laws § 257.1107

Sec. 7. (1) Subject to section 8, where a person recovers in any court in this state a judgment for damages on account of injury to or the death of any person or property damage occasioned in this state by an uninsured motor vehicle owned or operated by the judgment debtor within this state, upon the determination of all proceedings, including appeals, he may make application, in the form prescribed by the secretary and the secretary shall pay the amount of the judgment or of the unsatisfied portion thereof, subject to the limitations provided in this act with respect to death or personal injury and the amount of the judgment or of the unsatisfied portion thereof, in excess of $200.00, with respect to property damage out of the fund. (2) Where an application is made under this section, the secretary, at any time within 30 days of the receipt of the application, may give written notice to the applicant of any objection to payment of such judgment or any part of it. Where the secretary gives the notice the applicant may apply to the court entering judgment for a finding or determination in respect of any matter in connection with the application for payment out of the fund. (3) The secretary shall not pay out of the fund any amount in respect of a judgment unless the judgment was given in an action brought against all persons against whom the applicant might reasonably be considered as having a cause of action in respect of the damages in question and prosecuted against every such person to judgment or dismissal.