(1) In all cities and some towns, the mayor, or the manager in those cities operating under the commission-manager plan, shall nominate and, with the consent of the city council or commission, appoint three residents of such city or town who shall have the qualifications required by law to hold a municipal office therein and who shall constitute a board to be known by the name of "police commission".
(2) This section shall apply to organized police departments in every city and town of the state which have three or more full-time law enforcement officials, regardless of the form of government under which said city or town may be operating or may at any time adopt.