Any town at any annual meeting, under an article in the warrant for said meeting, may vote to elect by ballot one or more permanent constables or police chiefs or other police officers for full-time duty in said town and may rescind such action in like manner. No election of such permanent constable or police chief or police officer shall be held until the next succeeding annual meeting after the vote of the town. Any police chief or police officer or constable elected at an annual meeting may serve a one-year, 2-year, or 3-year term, as determined by the town at such annual meeting.