Mich. Comp. Laws § 78.22

Sec. 22. When any person has committed or is suspected of having committed any crime or misdemeanor within a village, whether incorporated under the provisions of this act or under an existing charter of the village heretofore granted or passed by the legislature for the government of a village, or has escaped from any prison of such a village, the police officers of such village shall have the same right to pursue, arrest and detain such person without the village limits as the sheriff of the county.