Conn. Gen. Stat. § 47-50: Division of fence by selectmen.

When a fence between adjoining proprietors has never been divided and either refuses to divide it, the other may call on the selectmen to make a division, who shall set out, in writing, the better part to him who erected it or to the party holding under him; and the cost, certified by the selectmen in writing, shall be paid by him who refused to make such division. Such division, when recorded in the town where the land lies, shall be binding on the parties.