New York Consolidated Laws, Legislative Law - LEG § 37. Time of convening an extraordinary session

Upon receipt of a perfected concurring petition by the temporary president or the speaker, as the case may be, or upon the receipt of a perfected joint petition by both the temporary president and the speaker, the legislature shall convene in an extraordinary session at noon on the first Monday after the first Tuesday after the last day for the return of signatures on such petition, or on any other day jointly agreed upon by the temporary president and the speaker, but no later than the second Monday after such Tuesday.  The secretary and clerk shall forthwith notify the members of the respective houses and the governor of the date and time when the legislature shall convene, and of the subjects to be considered, as enumerated in the perfected joint or concurring petition.