Mich. Comp. Laws § 600.828

Sec. 828. In a probate court district a probate judge who holds court in a county other than the county of his residence shall be reimbursed for his actual and necessary expenses incurred in so holding court upon his certification of the expenses to the state court administrator and upon approval by the state court administrator. Upon allowance, the sum shall be paid out of the general fund of the state in accordance with the accounting laws of the state.