N.Y. County Law § 280-T
At any time after the establishment of a district pursuant to this article, the maximum amount authorized to be expended for the original improvement in such district may be increased by a resolution of the governing body provided a petition requesting such increase executed and acknowledged in accordance with section two hundred eighty-d is presented to the governing body, and provided the governing body shall, after a public hearing called and held in the manner prescribed by section two hundred eighty-e, determined that it is in the public interest to authorize the increase of such maximum amount and provided the comptroller of the state of New York shall have made, prior to such public hearing, an order approving the increase of such maximum amount as stated in the petition. The order of the comptroller shall be prepared in duplicate and one copy thereof filed in the office of the department of audit and control and the other copy in the office of the clerk of the governing body of the county in which the district is located.
If zones of assessment have been established, such resolution of the governing body shall provide for the allocation of such increase as between such zones of assessment, and the notice of such public hearing shall state such allocation.
N.Y. County Law § 280-T