Any two or more towns, cities or boroughs may, by vote of their legislative bodies, vote to form a district for the performance of any municipal function which the constituent municipalities of such district may, under any provision of the general statutes or of any special act, perform separately. The affairs of any such district shall be managed by a board consisting of two members from each constituent municipality appointed by the board of selectmen of towns, the council or board of aldermen of cities and the board of burgesses of boroughs. Any town, city or borough having a population of more than five thousand inhabitants as determined by the last-completed federal census shall be entitled to one additional representative for each additional five thousand population or part thereof. The board shall, at its first meeting, determine by lot which members shall serve for one, two or three years, provided the terms of office of not more than fifty per cent of the board shall expire in any one year. Thereafter, the terms of office shall be for three years. Such board shall choose by ballot from its membership a chairman, a secretary and a treasurer. Such treasurer shall give bond to the board to the satisfaction of its members, the cost of such bond to be borne by the board.