Yes you can. The jury is allowed to review all of the evidence during deliberation, and trial testimony is evidence. It is at the judge's descretion as to what evidence the jury requests as to whether or not they can review it by considering why they want to review it, how much of it they should be given to review, etc. However, when it comes to trial testimony, it may be impossible for the jury while in deliberations to review certain trial testimony if that testimony has not yet been typed up, BUT the judge can have trial testimony that has not yet been typed up read in court by the court reporter from their "notes" as sometimes occurs during trial.
What the court reporter is typing up during testimony is more like a shorthand rather than regular typed out words, so the court reporter would be the only person able to decifer these "notes" in order to translate that information back as regular English words. The judge can also have the court reporter type up certain sections of trial testimony for the jury to review if what the jury requests to review is a small section though it would be more likely that the judge would just have the court reporter read out to the jury in court whatever section of testimony the jury requested to review and the jury members can then take notes on whatever it is about the testimony they were interested in if they want.
I'm not sure where anyone is getting that trial testimony can't be reviewed by a deliberating jury. Trial testimony is evidence, and the jury is always entitled to review all the evidence during deliberations.
The only example I can think of what a judge would not allow a jury to review during deliberations is testimony that for whatever reason was stricken from the record by the judge and the jury instructed at the time they should disregard or testimony that was given before there was an objection voiced and that objection concerning whatever the witness or attorney was saying was sustained.
http://nccriminallaw.sog.unc.edu/?p=4133
