N.Y. Mun. Home Rule Law § 21
Every local law shall be certified by the clerk after its passage by such body and shall be presented to the elective chief executive officer, if any, for approval by him. If such officer approves it, he shall sign it and return it to such clerk; it shall then be deemed to have been adopted. If he disapproves 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 legislative body at its next regular meeting and such objections shall be entered in its record, journal or minutes of proceedings. The legislative body within thirty days thereafter may reconsider the same. Such an elective chief executive officer who is a member of the legislative body shall not be entitled to vote on such reconsideration. If after such reconsideration such local law is repassed by a vote of at least two-thirds of the total voting power of the legislative body, exclusive of such officer, it shall be deemed adopted, notwithstanding the objections of such officer. Only one vote shall be had upon such reconsideration. The vote shall be taken by ayes and noes, and the names of the members present and their votes shall be entered in the record, journal or minutes of proceedings. If within thirty days after a local law shall have been presented to him such officer shall neither approve it nor return it to the clerk with his objections, it shall be deemed to be adopted in like manner as if he had signed it. At any time prior to such adoption or to the return of a local law by such officer, as the case may be, the legislative body may recall the same and reconsider its action thereon.
N.Y. Mun. Home Rule Law § 21