N.Y. Legislative Law § 37

§ 37. Time of convening an extraordinary session. Upon receipt of a\nperfected concurring petition by the temporary president or the speaker,\nas the case may be, or upon the receipt of a perfected joint petition by\nboth the temporary president and the speaker, the legislature shall\nconvene in an extraordinary session at noon on the first Monday after\nthe first Tuesday after the last day for the return of signatures on\nsuch petition, or on any other day jointly agreed upon by the temporary\npresident and the speaker, but no later than the second Monday after\nsuch Tuesday. The secretary and clerk shall forthwith notify the members\nof the respective houses and the governor of the date and time when the\nlegislature shall convene, and of the subjects to be considered, as\nenumerated in the perfected joint or concurring petition.\n