Mich. Comp. Laws § 331.101
The several boards of county supervisors of this state may raise by a tax to be levied on the property of said county, subject to taxation for county purposes, a sum of money to be used for constructing or maintaining or assisting to construct or maintain any hospital or sanitarium within said county. The said board of supervisors shall designate the hospital or sanitarium for which the moneys so raised are to be used: Provided, That any county not having within its boundary a hospital or sanitarium or any county though having a hospital or sanitarium within its boundary wishing to act in conjunction with any other county or counties for the purposes herein provided, may, in the judgment of the board of supervisors, use said moneys so raised in such combined undertaking of said several counties.
MCL 331.101