N.Y. Gen. City Law § 35
For the purpose of preserving the integrity of such official map or plan no permit shall hereafter be issued for any building in the bed of any street or highway shown or laid out on such map or plan, provided, however, that if the land within such mapped street or highway is not yielding a fair return on its value to the owner, the board of appeals or other similar board in any city which has established such a board having power to make variances or exception in zoning regulations shall have power in a specific case by the vote of a majority of its members to grant a permit for a building in such street or highway which will as little as practicable increase the cost of opening such street or highway, or tend to cause a change of such official map or plan, and such board may impose reasonable requirements as a condition of granting such permit, which requirements shall inure to the benefit of the city. Before taking any action authorized in this section, the board of appeals or similar board shall give a hearing at which parties in interest and others shall have an opportunity to be heard. At least fifteen days notice of the time and place of such hearing shall be published in an official publication of said city or in a newspaper of general circulation therein. Any such decision shall be subject to review by certiorari order issued out of a court of record in the same manner and pursuant to the same provisions as in appeals from the decisions of such board upon zoning regulations.
Where a proposed street widening or extension has been shown on such official map or plan for ten years or more and the city has not acquired title thereto, the city may, after a hearing on notice as hereinabove provided, grant a permit for a building and/or structure in such street or highway and shall impose such reasonable requirements as are necessary to protect the public interest as a condition of granting such permit, which requirements shall inure to the benefit of the city.
N.Y. Gen. City Law § 35