Mich. Comp. Laws § 168.851
If it shall appear on the canvass of the votes polled at any election canvassed by the board of county canvassers that 2 or more persons have received an equal number of votes for the same office, and that a failure to elect to any office is caused thereby, the election to the office shall be determined in the following manner: The board of canvassers for the county in which such election was held shall appoint a day for the appearance of all affected persons before the county clerk for the purpose of determining by lot among such persons the right to the office, and shall cause notice thereof to be given to all the persons interested. The county clerk shall prepare as many slips of paper as there are such persons, and write the word "elected" on as many slips of paper as there are offices to be filled, and the words "not elected" on the remaining slips, and fold the same so as to conceal the writing and so that they may appear as near alike as possible. The slips shall be placed in a box and, at the time and place appointed for the drawing of the lots, each of the persons aforesaid may draw 1 of the slips from the box, and any person drawing a slip on which is written the word "elected" shall be deemed legally elected to the office in question and the county clerk shall forthwith give him a certificate of election. The county clerk may appoint any person present to draw a slip for any affected person who fails to appear at the time specified in the notice. If the office of county clerk is in question, the drawing shall take place before the sheriff of the county. Such determination, however, shall not preclude the right of a defeated candidate to a recount of the votes cast as provided in chapter 36.
MCL 168.851