N.Y. Criminal Procedure Law § 310.70
1. If a deliberating jury declares that it has reached a verdict with respect to one or more but not all of the offenses submitted to it, or with respect to one or more but not all of the defendants, the court must proceed as follows:
(b) If the court is satisfied that there is a reasonable possibility of ultimate agreement upon any of the unresolved offenses with respect to any defendant, it may either:
2. Following the rendition of a partial verdict pursuant to subdivision one, a defendant may be retried for any submitted offense upon which the jury was unable to agree unless: