Conn. Gen. Stat. § 47-56
When adjoining proprietors are unable to agree about erecting a division fence and there is a dwelling house on the lot of one proprietor within one hundred rods of the dividing line, he may notify any two selectmen of the town in which such lot is situated or, if it is in more than one town, then one selectman from each town, who shall give written notice to the parties of the time and place of a hearing in regard to such fence; and the proprietor of such lot may, upon the terms named by the selectmen, erect a better fence than is required by law, and the adjoining proprietor shall pay such part of the expense as he would pay for the erection of an ordinary sufficient fence, but shall be allowed the value of his part of the existing division fence appraised by the selectmen. The expense of maintaining such better fence beyond that of an ordinary sufficient fence shall be defrayed by the owner of such lot, who shall also pay the fees of the selectmen. Such selectmen shall make a written certificate of their doings and leave a copy with each proprietor; and the party erecting the fence may recover of the other party the amount to be paid by him if not so paid within thirty days after the erection of such fence.
Conn. Gen. Stat. § 47-56
(1949 Rev., S. 7165.)