Mich. Comp. Laws § 331.210
Prior to the regular October session of the board of supervisors in each year, it shall be the duty of the board of trustees of the hospital or institution to make and present to the board a full and detailed report of the operations during the preceding year and of the receipts and disbursements. Said board of trustees shall present to said board of supervisors any information said board of supervisors may request concerning said hospital or institution. Said board of trustees shall present to the board of supervisors an estimate of the funds necessary to be raised in such county for the ensuing year. Thereupon, the board of supervisors, subject to the provisions of this act, shall vote such amount as it shall deem necessary to be raised by taxation. No moneys shall be expended by the board of trustees, except as appropriated by the board of supervisors. In case it is deemed expedient by any board of supervisors to raise in any 1 year, either for acquisition, construction, maintenance or operation purposes, an amount in excess of 1 mill on each dollar of assessed valuation of said county, the question of raising by taxation or borrowing such amounts as may be deemed necessary, shall be submitted to the electors of the county at any general election or at a special election called for that purpose. Said question shall be submitted and election held and conducted and returns thereof canvassed and declared in the same manner as is or may be provided by the general election law for the submission and determination of the question of issuing county bonds. If a majority of the electors of the county voting thereon authorize the raising of such additional sum or sums, the board of supervisors shall by resolution direct the raising of the same by taxation.
MCL 331.210