Mich. Comp. Laws § 730.507
Any city may by ordinance fix the compensation to be paid substitute municipal judges for such services, the procedure to be followed in calling upon them to act, and the time and manner of compensation: Provided, however, That the legislative body of any city may provide in its budget an appropriation for the payment of substitute judges, and when such appropriation is provided, the municipal judge of such city may engage the services of such substitute judges as may be necessary to carry out the duties of the court, and upon presentation of a voucher for such services, approved by the municipal judge requesting such services, such substitute judge shall be compensated from the appropriation so made: Provided further, That unless a city shall provide by ordinance for the compensation of substitute judges, or make an appropriation in its budget for such substitute judicial services, no such substitute judge shall be entitled to compensation from such city.
MCL 730.507