It shall be the duty of the police department of the city to suppress all riots, disturbances, and breaches of the peace; to arrest all persons fleeing from justice; to apprehend upon view any person found in the act of committing any offense against the laws of the State or violating the ordinances of the City, or any provisions of this charter, or in any manner involving the breach of peace, and to take the offender so arrested before the proper magistrate or officer to be punished; to make complaint before the proper magistrate of any person known or believed by it to be guilty of any crime or violation of the laws of this State, the ordinances of this City, or the provisions of this charter, and to serve all processes that may be delivered to it for that purpose; and generally to perform all such duties as may be required of it by the police chief under the supervision of the city manager for the good government of the City. It shall be the duty of the police department of the City to see that all ordinances and regulations of the City made for the preservation of peace and good order and for the safety and protection of the inhabitants of the City are promptly enforced. For the preservation of peace and good order, and as peace officers, each policeman shall be and is hereby vested within the territorial limits of the City with all the powers conferred by law upon sheriffs for the preservation of peace and good order, and shall have and is hereby vested with all the powers given by law to constables for such purposes. Such police officers shall have power to serve and execute all processes directed or delivered to them, in all proceedings for violation of the ordinances of the City. Such processes may be served by such police officers anywhere within the County of Wayne. When any person has committed or is suspected of having committed any crime or misdemeanor within the city or has escaped from the city jail, the police officers of the city shall have the same right to pursue, arrest, and detain such persons outside the city limits as the sheriff of the County.