Should jurors be allowed to ask questions to witnesses during a criminal trial?
I don't know if you're asking this from the perspective of
a) Should as in "is it right and proper?" or
b) Should as in "I don't know if they can"
So just in case.... They can already and yes, it is right and proper. But with rules.
The jury are the most important people in the courtroom in respect of the law. They determine guilt or innocence, so they have to be certain that they are getting that crucial decision right.
If any of them feel that a piece of information is missing which may be provided by the witness then it is their duty to bring this to the attention of the judge.
The caveat is this. Juries will not usually be made up of legally trained people, so to prevent improper questions which may be subject to legal technicalities; the question must be raised to the judge first (the jury will write a note). The judge may or not send them out whilst they deliberate with all counsel. If the question is agreed, the judge will put it to the witness on their behalf.
If not agreed, the judge will explain to the jury that their question cannot be answered by that witness. It is up to the judge as to how much to reveal about the reasons for refusal.
So in summary, absolutely yes, juries should be allowed to raise their own questions. But not to question the witness directly themselves. They may cause a mistrial.
Depends on the country and its judicial traditions.
In most countries, the jury as a whole may put questions to the witness but there are strict rules as to how it's done.
In most countries too, the reality is that jury questions are at the discretion of the judge in session.
However, Japanese courts allow the jury the right to put questions to the prosecution, the defendant and the witnesses.
That's because Japanese courts technically don't have a jury. The ‘jurors' in fact are selected to perform their civic judicial duty as lay judges to assist the professional judge(s).
As lay judges, they are in their right to ask questions. Again, their right is also at the discretion of the head judge in session, if that doesn't sound like a contradiction.