When the line on which a division fence is to be made or maintained is the line between two towns, and the parties do not agree upon the division, the same shall be determined by a board of fence viewers consisting of one or more from each of the towns. Such board of fence viewers shall give notice to the parties, make the division, and make a certificate as provided in section 3811 of this title. Such certificate shall be valid against the parties, their heirs, and assigns, if recorded in the office of the town clerk in each of the towns.