New York Laws
Article 41 - Trial by a Jury
4102 - Demand and Waiver of Trial by Jury; Specification of Issues.

(b) Specification of issues. In his demand a party may specify the
issues which he wishes tried by jury; otherwise he shall be deemed to
have demanded trial by jury of all issues so triable. If he has demanded
trial by jury of only some of the issues, any other party within ten
days after service of the demand may serve and file a demand for trial
by jury of any other issues in the action so triable.
(c) Waiver. A party who has demanded the trial of an issue of fact by
a jury under this section waives his right by failing to appear at the
trial, by filing a written waiver with the clerk or by oral waiver in
open court. A waiver does not withdraw a demand for trial by jury
without the consent of the other parties. A party shall not be deemed to
have waived the right to trial by jury of the issues of fact arising
upon a claim, by joining it with another claim with respect to which
there is no right to trial by jury and which is based upon a separate
transaction; or of the issues of fact arising upon a counterclaim,
cross-claim or third party claim, by asserting it in an action in which
there is no right to trial by jury.
(d) Local rules. The chief administrator of the courts may by rule
provide that a party shall be deemed to have demanded trial by jury by
filing a note of issue not containing an express waiver of trial by
jury.
(e) Relief by court. The court may relieve a party from the effect of
failing to comply with this section if no undue prejudice to the rights
of another party would result.