Mich. Comp. Laws § 730.513
When this act becomes effective in any city, the judges of the municipal court of such city shall designate 1 of their number to act as presiding judge for such time as may be fixed by rule. In any city which has 2 municipal judges, they shall alternate as presiding judge, for such periods of time as may be fixed by rule, and in the absence or inability of the presiding judge, the other shall act as such. In any city which has more than 2 municipal judges, they shall be designated in such manner, and serve for such periods of time, as shall be fixed by rule, and in the absence or inability of the presiding judge, another shall act as such: Provided, however, That in any such city having 2 municipal judges, 1 of whom is an associate elected on a part-time basis, the one elected on a full-time basis shall be the presiding judge of said court. In any city which has more than 2 municipal judges, they shall be designated in such manner and serve for such periods of time as shall be fixed by rule. The presiding judge may designate some other judge of such court to act as such during his absence.
MCL 730.513