Section 21. By vote of a town meeting called for the purpose in any town at least sixty days before an annual meeting, or upon request by petition of ten per cent of the qualified voters of any town filed with the selectmen thereof at least sixty days before an annual town meeting, asking that the selectmen act as a water and sewer board, water commissioners, water and municipal light commissioners, municipal light board, sewer commissioners, park commissioners, board of public works, board of health, assessors, or commission of public safety, or perform the duties of such boards or officers or any of them or that cemetery commissioners, assessors, a superintendent of streets, a chief of the police and fire departments or board of health be thereafter appointed by the selectmen, the selectmen of such town shall include in the warrant for such annual meeting for submission to the voters such question or questions in the following form, to be placed on the official ballot in towns using such ballot:—

If a town, in which the selectmen are elected for terms of one year, shall vote in accordance with this section that its selectmen shall act as or perform the duties of any of the aforesaid boards or officers, it shall, at the next annual meeting, elect one selectman for one year, one for two years and one for three years, or, if five are to be elected, one for one year, two for two years and two for three years, and thereafter in either event shall elect them for terms of three years. Upon the election and qualification of the selectmen at such next annual meeting, and upon the appointment and qualification by oath of the officers herein authorized to perform the duties of any existing town board or officer, the term of office of such existing board or officer shall thereupon terminate, and all the duties, powers and obligations of said boards and officers shall be transferred to and imposed upon their successors.