N.Y. Civil Practice Law & Rules § 3402
Rule 3402. Note of issue. (a) Placing case on calendar. At any time after issue is first joined, or at least forty days after service of a summons has been completed irrespective of joinder of issue, any party may place a case upon the calendar by filing, within ten days after service, with proof of such service two copies of a note of issue with the clerk and such other data as may be required by the applicable rules of the court in which the note is filed. The clerk shall enter the case upon the calendar as of the date of the filing of the note of issue.