Mich. Comp. Laws § 92.4
Under the direction of the mayor and chief of police, and in conformity with the ordinances of the city and laws of this state, the police shall suppress riots, disturbances, and breaches of the peace; pursue and arrest a person fleeing from justice in any part of the state; apprehend a person in the act of violating a law of this state, or an ordinance of the city, involving a breach of the peace, and, unless the violation constitutes a civil infraction, take the offender before the proper court or magistrate, to be dealt with for the violation; make complaints to the proper officers and magistrates of any person known or believed by them to be guilty of the violation of the ordinances of the city or the penal laws of the state or to be responsible for a violation of an ordinance or law of this state designated as a civil infraction; diligently and faithfully to enforce all laws, ordinances, and regulations for the preservation of good order and the public welfare as the council may ordain; and serve process directed or delivered to them for service. For such purposes, the chief of police and every police officer have the powers of constables and may arrest, upon view and without process, a person in the act of violating an ordinance of the city involving a breach of the peace, unless the violation constitutes a civil infraction, or of committing a violation of a criminal law of this state. The chief of police and a police officer may serve and execute process in a proceeding for a violation of an ordinance of the city, and also any other process that a constable may serve.
MCL 92.4