N.Y. Second Class Cities Law § 162
In all cases of assessment for improvements the assessors shall include in the apportionment all the expenses connected with or which were incident to the making of the improvement and assessment. Whenever the amount apportioned shall exceed the actual cost of the improvement, including all expenses connected therewith or incidental thereto, the comptroller shall certify the amount of the surplus to the assessors and they shall thereupon declare a rebate and the excess shall be refunded pro rata to the persons who paid their assessments. If the amount assessed for any improvement shall be insufficient to cover the cost of the improvement, including all expenses connected therewith and incidental thereto, the comptroller shall certify the amount of the deficiency to the common council and assessors, and the common council and assessors shall forthwith cause to be assessed and levied the amount of such deficiency pro rata upon the property included within the original assessment and the same shall be assessed, levied and collected in like manner as other assessments of a like character.
N.Y. Second Class Cities Law § 162