(a) In a municipality, the duty of the chief of police and other officers of the police department is under the direction of the mayor.
(b) It is their duty to:
(1) Suppress a riot, disturbance, or breach of the peace;
(2) Pursue and arrest a person fleeing from justice in any part of this state;
(3) Apprehend a person in the act of committing an offense against the laws of the state or the ordinances of the city and forthwith bring the person before the proper authority for trial or examination; and
(4) Diligently and faithfully enforce at all times all laws, ordinances, and regulations for the preservation of good order and the public welfare as the city council may ordain. For this purpose, the chief of police and other officers of the police department have all the power of constables.