Minn. Stat. § 641.08: SUPERVISION.

When a sentence is for violation of a state law, and the prisoner is confined in a county jail, such labor shall be performed under the direction of the county board, and superintended by the sheriff, who shall furnish necessary materials and tools at the expense of the county, and the county shall be entitled to the benefit thereof. When the sentence is for a violation of an ordinance, bylaw, or regulation of a city, such labor shall be performed under the direction of its governing body, and superintended by the chief of police, who shall furnish the materials at the expense of such city, which shall be entitled to the benefit thereof.