Mich. Comp. Laws § 750.162
When any person is convicted under section 161 and sentenced to serve a term of imprisonment either in 1 of the state prisons or other penal institution, the warden of the prison or superintendent of said penal institution in which said person shall be confined shall, in case funds are available for such purpose, at the end of each and every week during the period of said term of imprisonment, pay over to any of the superintendents of the poor of the city or county in which the wife or children of such person resides, the sum of 2 dollars and 50 cents per week, if there be only a wife, and 75 cents per week additional for each minor child under the age of 17 years; if there be no wife and there are children under the age of 17 years, the sum of 2 dollars and 50 cents per week for the oldest child, and an additional sum of 1 dollar per week for each of the other children under said age in lieu of any earnings of such person while an inmate therein, said sums to be expended by said superintendent of the poor for the care and support of the wife or children of said person, as the case may be; and it shall be the duty of the superintendent of the poor of the city or county from which such person shall be committed to furnish the warden of the prison or superintendent of the penal institution in which said person is confined with a sworn statement, showing the names of the wife and children who are left dependent upon the city or county for support, their ages and the relation they bear to such convicted person.
MCL 750.162