The answer is “Maybe.”
Judges in New York have the ability to control what goes on in their courtroom. Some judges permit jurors to ask questions and others do not.
Of those judges who do permit jurors to ask questions, you should know that the jurors are not permitted to simply shout out a question anytime they want. Nor can they simply raise their hand and ask a question directly of the witness or of an attorney.
Instead, when jurors are permitted to ask questions they are required to write down the question, give the note to the court clerk or court officer who will then take the note and deliver it to the judge. The judge will then review the question and determine whether it should be asked.
If the judge decides the question is acceptable than he will ask the question of the witness or of the attorney.
The judge uses this filter process to make sure that the questions that are being imposed or legally correct and do not prejudice either of the parties.