In Supreme Court, a jury cannot be demanded until the filing of a note of issue, which does not happen until after discovery is complete (N. Rule 38 preserves the right to a jury trial in civil cases, requiring a specific demand within 14 days after the last pleading directed to the issue.Purpose of This Handbook The purpose of this handbook is to acquaint trial jurors with the general nature and importance of their role as jurors. Under New York law, you can demand a jury trial in many cases. Under New York law, you can demand a jury trial in many cases. The grand jury is included in the United States Constitution and the New. York State Constitution. Jury Demand: In certain kinds of cases, the parties are entitled to a jury trial. In New York, jury trials are allowed for many injury cases. In Supreme Court, a jury cannot be demanded until the filing of a note of issue, which does not happen until after discovery is complete (N.