Section 99. The mayor, selectmen, chief of police, or person however designated having the duties of a chief of police, or, in the absence of the chief of police, or person however designated having the duties of a chief of police, the commanding officer, may upon the request of the mayor, selectmen, chief of police, or person however designated having the duties of a chief of police, or in the absence of the chief of police or person however designated having the duties of a chief of police, the commanding officer of any other city or town, provide police officers, who shall have the authority of constables and police officers within the limits of such city or town, except as to the service of civil process, and, while exercising such authority within such limits, shall have the same immunities and privileges as when acting within their respective cities and towns; and the city or town providing said officers shall be entitled to receive from such city or town the amount paid to them for their service, including their necessary traveling expenses.