N.Y. High. Law § 199
When any part of a highway in any town of this state, not in an incorporated village or city, running between two or more villages or cities, has, because of the wearing away by a river or stream or any other natural cause, become narrower than the width required by statute, and is dangerous to the users of such highway, twelve or more resident taxpayers of such town may present a petition to the supreme court in the judicial district within which such town is situated. The petition shall describe the part of the highway proposed to be widened and state that such highway has become lessened in width by the action of a river or stream or other cause, that it is dangerous to the traveling public, that the widening and improvement of such highway is necessary for the public convenience and welfare, that the highway is an important leading road between two or more cities or villages, that the cost of such widening and improvement would exceed the sum of two thousand five hundred dollars and would be too burdensome on the town or towns otherwise liable therefor. Such petition shall be verified by at least three of the petitioners. On receipt of the petition by supreme court the court shall appoint a time and place for a meeting to hear all persons interested in the proposed widening of the highway. The court shall examine the part of the highway proposed to be widened, hear any reasons for or against such widening and ascertain the probable cost of the work. If the court shall determine that the proposed widening of the highway is necessary and that the cost thereof would be too burdensome for the town, exceeding in probable cost two thousand five hundred dollars, they shall notify the board of supervisors of the county of such decision. The board of supervisors shall thereupon cause one-half of the amount of the estimated cost to be raised by the county and paid to the supervisor of the town or towns in which that part of the highway proposed to be widened as aforesaid is located, and said supervisor shall apply the sum so received by him towards the payment of the cost of such widening. The balance of the expense shall be raised in the manner provided by law, by the town or towns in which that part of the highway proposed to be widened as aforesaid is located.
N.Y. High. Law § 199