N.Y. County Law § 299-R
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 ninety-nine-n of this article, in such district may be increased by resolution of the board of supervisors or county legislature and provided said body shall, after a public hearing called and held in the manner prescribed by section two hundred fifty-four of this chapter, determine 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. 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 county in which the district is located.
N.Y. CountyLaw § 299-R