Mich. Comp. Laws § 801.209

Sec. 9. In every county having such agreement, it shall be the duty of every court by whom any person, for any crime or misdemeanor not punishable by imprisonment, in the State prison, may be sentenced for any term of not more than 6 months, to sentence such person to the work farm, factory, or shop there to be received, kept, and employed in a manner prescribed by law and the rules and discipline of the work farm, factory, or shop; and by such warrant and commitment to cause such persons to be forthwith conveyed by some proper officer to work farm, factory, or shop.