Michigan Compiled Laws, Chapter 400. Social Services § 400.70

Sec. 70. The county board of supervisors shall, within its discretion, make such appropriations as are necessary to maintain the various welfare services within the county, as provided in this act, and to defray the cost of administration of these services. In the case of a district department of social welfare the county board of supervisors of each county forming a part of said district shall appropriate funds necessary to care for the welfare services of such county, and the administrative expenses of the district department shall be defrayed by all of the counties in said district in the proportion that the population of each county, according to the last federal census, bears to the population of the entire district.