Mich. Comp. Laws § 331.202

Sec. 2. Hereafter it shall be competent and lawful for the board of supervisors of any county in this state now or hereafter having a population of more than 100,000 as determined by the last federal decennial census or by any federal decennial census hereafter taken, to acquire, own, construct, establish, maintain and operate a hospital for the treatment of persons suffering from contagious and infectious diseases and for the treatment of indigent persons suffering from any physical ailment or impairment, and may contain a psychiatric ward for mentally ill patients, both non-indigent and indigent, provided that such a ward has been approved by the state department of mental health. Said board of supervisors, in the case of construction of such hospital, shall designate the site on which such hospital shall be placed. The board of supervisors shall also determine the sum or sums of money to be appropriated for the acquisition, ownership, construction, establishment, maintenance, operational and equipment purposes.