Such board shall choose one of its members to be chairman thereof and shall choose a clerk. If such officers are not chosen within one month after the appointment or election of the board because of a tie vote of the members, the board of selectmen or chief executive authority of such town shall choose such officers from the membership of the board. At all meetings of the board four members shall constitute a quorum and the concurrence of three votes shall be necessary for the transaction of business. The board may hold such regular and special meetings as may be advisable at any time upon giving at least twenty-four hours’ notice to each member before the time of such meeting, provided, except where otherwise provided by special act or charter, in any case involving a vote of the board on an appropriation, or a transfer within an existing appropriation, of an amount not exceeding one thousand dollars, the chairman or, in his absence, the clerk or any two members, may, in lieu of calling a meeting of the board, poll the members thereof; and the clerk shall cause to be prepared and filed with the town clerk, within two weeks, a statement of the result of such poll. Four polled members shall constitute a quorum for such purpose and a concurring vote of three such members shall be sufficient for the transaction of business. Every member so polled shall deliver, by mail or otherwise, to said clerk, within twenty-four hours after the poll, a written statement signed by him stating how he voted on the question. The clerk of the board shall issue a call for a special meeting either at the direction of the chairman of the board or upon a written request of any two members thereof. The clerk shall cause to be prepared and filed with the town clerk a copy of the minutes and records of each regular and special meeting held, within two weeks from the date of such meeting.