The Board of Trustees of the corporation shall have the power to lay out, alter, maintain, or discontinue any sidewalk in the Village, and appraise and settle the damage therefor, causing their proceedings to be recorded in the Town Clerk's office in the Town; provided that the trustees, in laying out, altering, and maintaining, or discontinuing, any such sidewalk, shall be subject to the same regulations, and in all respects shall proceed in the same manner, as the selectboard of towns in laying out, altering, and discontinuing highways; and any party aggrieved shall be entitled to the same redress to which they would be entitled if the same had been done by the Selectboard of the Town of Cambridge.