The Moderator, Prudential Committee, Clerk-Treasurer, and Justices of the Peace residing in the District shall constitute a Board of Civil Authority in the District. The Board of Civil Authority shall have the same authority and power to abate taxes as the board of civil authority in towns. The Board of Civil Authority shall be responsible for conducting elections and shall decide all questions as to the eligibility of a person to vote in a district meeting. The members of the Board of Civil Authority present and acting at any meeting shall constitute a quorum in which to act.