§ 303. Settlement of disputes. If disputes arise between the owners of adjoining lands, concerning the liability of either party to make or maintain any division fence, or the proportion or particular part of the fence to be made or maintained by either of them, such disputes shall be settled by any two of the fence viewers of the town, one of whom shall be chosen by each party; and if either neglect, after eight days' notice, to make such choice, the other party may select both. The fence viewers, in all matters heard by them, shall see that all interested parties have had reasonable notice thereof, and shall examine the premises and hear the allegations of the parties. If they cannot agree, they shall select another fence viewer to act with them, and the decision of any two shall be reduced to writing, and contain a description of the fence, and the proportion to be maintained by each, and shall be forthwith filed in the office of the town clerk, and shall be final upon the parties to such dispute, and all parties holding under them.