Mich. Comp. Laws § 400.58b
The state department in accordance with its rules and regulations may pay for medical care that a recipient of aid to the blind, aid to disabled, aid to dependent children, or old age assistance, receives in the county medical care facility. Other persons admitted to care in the facility shall be charged for the cost of their care to the extent of their financial ability as determined by the county department and such financial ability shall not preclude their eligibility for such care. Prior consideration shall be given to any person who comes within the definition of a "poor person" set forth in section 1 of chapter 1 of Act No. 146 of the Public Acts of 1925, as amended, being section 401.1 of the Compiled Laws of 1948. No poor persons as so defined shall be refused admittance to a county medical care facility if there are then within such county medical care facility persons who are not senile and who are paying the total cost of their care.
Any county department which shall accept state financial aid for capital expenditures related to the establishment, extension or improvement of its facilities shall accept for care any patient eligible for admission as provided in section 58a, and having a domicile in the county and any patient for whom care is requested by the state department because of being found in the county without either a known domicile in the state or a place of residence outside the state to which he may be returned.
Direct state financial aid to meet part of the cost of capital expenditures for the establishment, extension or improvement of a county medical care facility may be provided from the general funds of the state or from such federal funds as may be made available in the following manner: The county social welfare board with the approval of the county board of supervisors will make an application to the state department as otherwise provided in section 58 but shall make in addition, a showing of need, in the same manner as provided in section 18, that it is unable to meet all of the capital expenses of a county medical care facility. The state department shall determine the percentage of the total capital cost of the facility which the county will be unable to meet and shall request from the legislature an appropriation from the general fund of the state or such federal funds as may be made available for this purpose to meet this amount. Requests of the legislature from the state department for such appropriations shall be separate items for each medical care facility. The amount of state aid actually granted the county by the state department shall not exceed (1) the amount appropriated by the legislature in respect to the amount of the item in the budget, or (2) the percentage of state aid required as previously determined by the state department, whichever is the lesser.
To defray the cost of construction in the establishment or extension of the medical care facility, the board of supervisors may raise in any 1 year a sum not exceeding .1 mill of each dollar of assessed valuation of the county, such tax to be regarded as a special tax collected in the same manner as other county charges, and moneys received therefrom shall be transmitted to the treasurer of the county who shall deposit same in a special fund to be used solely for the purposes for which the tax is spread. Money expended for construction in the establishment or extension of the facility shall be paid out by the county treasurer on the order of the county social welfare board.
MCL 400.58b