Mich. Comp. Laws § 400.59
All applications for aid, relief or assistance provided under this act shall be made to the county department of social welfare in such manner and upon such forms as may be prescribed by the state department. When any person applies for or requires public aid as a poor person under this act other than hospitalization or those forms of aid financed in whole or in part by federal funds, the county department shall ascertain the legal settlement and domicile of the person. The county department shall ascertain the settlement and domicile of other persons when requested by the county health department or by the state health commissioner. Except as otherwise provided in this act, general relief granted to persons with a legal settlement in this state may be charged to the county of domicile. The sending of notices, billings and appeals in respect to charges to the county of domicile, shall be made in accordance with regulations of the commission. Wherever in this act a chargeback or return to the county or city of "settlement" or "legal settlement" is authorized a chargeback or return to the county or city of "domicile" shall be deemed to be intended. Hospitals, jails, nursing homes, convalescent homes, homes for the aged and prisons are not places of domicile. General relief and hospitalization granted to persons who, while receiving assistance under this act, move into a county to receive care in a home for the aged, convalescent home or other institution shall be a charge against the county of their domicile just prior to the move regardless of other provisions of this act and even though domicile in the home for the aged or other institutions is intended. Temporary relief granted to persons with no settlement in this state shall be at the expense of the county where found. In the case of persons illegally brought or induced to come into the county, necessary relief shall be a charge against the county where they were living when transported or induced to move.
MCL 400.59