N.Y. Village Law § 6-620
Whenever the owner or occupant of lands adjoining a street constructs along such street a sidewalk of stone, cement, brick or other similar materials to be approved by the board of trustees, and the board consents to bear a portion of the expense of construction thereof, the board of trustees may pay to such owner or occupant a sum to be fixed by the board of trustees not exceeding one-half of the actual and necessary expense of constructing such sidewalk. Before the board of trustees shall so consent to bear a portion of the expense of construction of any such sidewalk, it shall fix the proportionate amount that shall be paid by the village for all walks of the same kind which may thereafter, with such consent, be constructed therein; and such proportionate amount may be changed from time to time thereafter by the board of trustees, but at no time within one year from the date of the last fixing or changing thereof.
N.Y. Village Law § 6-620