Mich. Comp. Laws § 330.1932
The several counties of the state have power and authority, by resolution of the county board of commissioners, to provide for the care, custody, and maintenance of developmentally disabled persons within the counties and for this purpose counties may raise money by tax or by loan and issue bonds of the county to secure the repayment of the loan in the manner and within the limits provided by law for the erection of buildings and for the purchase of equipment. Counties may raise by tax, in the manner and within the limits provided by law, the sum needed from year to year, for the support, maintenance, and care of developmentally disabled persons admitted to the care of any facility maintained by the counties under and by authority of law.
MCL 330.1932