If the selectmen of any town and any person interested in the layout, opening, grading or alteration of any highway or private way in such town cannot agree as to the damages sustained by, or the benefits accruing to, such person thereby, the selectmen shall apply to any judge of the Superior Court who, having caused reasonable notice to be given to the parties interested, shall appoint a committee of three disinterested electors to estimate and assess each person injured or benefited the damages sustained by or the benefits accruing to such person by such layout, opening, grading or alteration of such way. Such committee, having thereupon given at least ten days’ notice to the parties interested of the time and place of its meeting, shall, under oath, make such estimate and assessment and immediately report its actions to the superior court in the judicial district in which the land is situated. Notice of the time and place of the meeting of such committee may be given to the parties interested, if they are residents of the state, personally, or by leaving written notices at their respective places of abode, or by depositing in the post office, postage paid, notices addressed to them respectively; or, if they are nonresidents, by like notice to the person having charge of the land. Any person interested in such estimate or assessment may appear before said court and remonstrate against the acceptance of such report for any irregularity or improper conduct; and thereupon the same proceedings shall be had by said court in accepting or rejecting such report, and in ordering a jury to reassess the damages and benefits, or either, as provided in the case of applications brought to said court against towns for the layout or alteration of highways; and such jury, and the court in acting upon the report of such jury, shall proceed as in the case of such applications.