When the selectmen of any town refuse to lay out any necessary highway or to make any necessary alterations in any existing highway, unless such refusal is based on a designation of the existing highway as a scenic road pursuant to § 7-149a, any person may prefer an application therefor to the superior court for the judicial district in which such town is located, accompanied by a summons, signed by proper authority, to be served in the same manner as civil process on one of such selectmen, to appear and be heard thereon; and, unless the parties agree as to the judgment to be rendered, such application shall be heard and decided by a committee of three disinterested persons to be appointed by the court, at such time and place and with such reasonable notice to those interested therein as said court orders. If such committee finds that such highway or alteration will be of common convenience and necessity, it shall survey and lay out the same and estimate the damages sustained by or the special benefits accruing to each person by the layout of a new or the alteration of an existing highway, and report in writing its doings to said court.