New York Consolidated Laws, Civil Practice Law and Rules - CVP § 4109. Peremptory challenges

The plaintiff or plaintiffs shall have a combined total of three peremptory challenges plus one peremptory challenge for every two alternate jurors.  The defendant or defendants (other than any third-party defendant or defendants) shall have a combined total of three peremptory challenges, plus one peremptory challenge for every two alternate jurors.  The court, in its discretion before the examination of jurors begins, may grant an equal number of additional challenges to both sides as may be appropriate.  In any case where a side has two or more parties, the court, in its discretion, may allocate that side's combined total of peremptory challenges among those parties in such manner as may be appropriate.