N.Y. Educ. Law § 2005
Whenever the time for holding the annual meeting in a school district shall pass without such meeting being held, a special meeting, to be held on the date specified for a school budget revote pursuant to subdivision three of section two thousand seven of this part, shall thereafter be called by the trustees or by the clerk of such district for the purpose of transacting the business of the annual meeting; and if no such meeting be called by the trustees or the clerk within ten days after such time shall have passed, the district superintendent of the supervisory district in which said school district is situated or the commissioner of education may order any inhabitant of such district to give notice of such meeting in the manner provided in section two thousand one of this part, and the officers of the district shall make to such meeting the reports required to be made at the annual meeting, subject to the same penalty in case of neglect; and the officers elected at such meeting shall hold their respective offices only until the next annual meeting and until their successors are elected and shall have qualified. Notice of such annual meeting shall comply with the requirements of section two thousand three or section two thousand four of this part by publishing such notices once in each week within the two weeks next preceding such special meeting, the first publication to be at least fourteen days before such meeting and any required posting to be fourteen days before the time of such meeting. If the qualified voters at such special district meeting defeat the school district budget, the trustees or board of education shall adopt a contingency budget pursuant to section two thousand twenty-three of this part. Notwithstanding any other provision in law, the trustees or board of education following the adoption of a contingency budget may call a special district meeting for a second vote on the proposed budget pursuant to the requirements of subdivision three of section two thousand seven or subdivision three of section two thousand six of this chapter.
N.Y. Educ. Law § 2005