N.Y. Second Class Cities Law § 38
Every ordinance of the common council shall immediately after its passage be separately engrossed and signed by the president and attested by the clerk. The clerk shall thereupon present the same to the mayor. If the mayor approve it he shall sign it and return it to the clerk, and the ordinance shall thereupon take effect. If he disapprove it, he shall return it to the clerk with his objections stated in writing, and the clerk shall present the same with such objections to the common council at its next regular meeting. The common council may, within thirty days thereafter, reconsider the same; if, after such reconsideration, three-fourths of all the members of the common council shall vote to pass the ordinance the same shall take effect notwithstanding the objections of the mayor, unless a greater number of members were necessary according to the provisions of this chapter for the original passage of the ordinance, in which case unless as many members as were requisite for the original passage of the ordinance shall vote to pass the ordinance it shall not take effect. If any ordinance shall not be returned by the mayor to the clerk within ten days after it shall have been presented to him, or if such ordinance shall be returned within such period without the mayor's approval or disapproval, the same shall take effect in like manner as if the mayor had approved and signed it. If any ordinance presented to the mayor contains several items of appropriation of money or embraces more than one distinct subject, the mayor may approve the provisions relating to one or more items or one or more subjects and disapprove the others. In such case those items or subjects which he shall approve shall take effect and he shall append to the ordinance at the time of signing it a statement of the items or subjects which he disapproves and said items or subjects so disapproved shall not take effect. He shall return to the clerk a copy of such statement and the items or subjects disapproved may be separately reconsidered by the common council and shall only become effective if again passed by it as above provided. All the provisions of this section in relation to ordinances disapproved by the mayor shall apply in cases in which he shall disapprove any item or subject contained in an ordinance appropriating money or embracing more than one distinct subject.
N.Y. Second Class Cities Law § 38