N.Y. County Law § 269
At any time after the establishment of a district pursuant to this article, the maximum amount authorized to be expended for the original improvement or for the original improvement, the plans for which have been amended or modified pursuant to section two hundred fifty-three-a of this article, in such district may be increased by a resolution of the board of supervisors on its own motion or provided a petition requesting such increase executed and acknowledged in accordance with section two hundred fifty-three of this article is presented to the board of supervisors, and provided the board of supervisors shall, after a public hearing called and held in the manner prescribed by section two hundred fifty-four of this article, determine that it is in the public interest to authorize the increase of such maximum amount and provided that whenever it is proposed or required that the county in which such district is located shall finance the cost thereof by the issuance of the bonds, notes, certificates or other indebtedness of the county therefor, or shall assume the payment of annual installments of debt service on obligations issued to finance the cost of facilities, pursuant to section two hundred sixty-two of this article, and the cost to the typical property or, if different, the cost to the typical one or two family home is above the average estimated cost to the typical properties or homes for the establishment of similar types of districts as may be annually computed by the state comptroller, 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 motion or 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 board of supervisors of the county in which the district is located.
If zones of assessment have been established, such resolution of the board of supervisors 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.
The resolution of the board of supervisors shall be subject to a permissive referendum in the same manner and extent as provided for in section two hundred fifty-six of this article.
N.Y. CountyLaw § 269