You will not be able to review trial testimony without purchasing a transcript if the DA will not permit you to review their records. Perjury is lying under oath so you are not in any risk of perjury so long as you are not under oath and do not intentionally lie.
Don't send a letter to the judge. It won't be read.
Nothing in a case progress through the appeal process requires or invites a letter to the trial court by any witness. Once the matter was noticed for appeal, the trial court no longer has any power (jurisdiction) over the case. The appeal is decided by the appellate court based on what is already in the record of the trial and procedural history. Nothing that you can say now in any letter will be considered by the appellate court, nor have any legal affect on the appellate result. There is no appropriate purpose to any correspondence by you to either the appellate or the trial court.
At some point in the appeal process, the transcript of the trial, proceeding or some relevant portion of it, may be filed with the appellate court. You can inquire of the clerk of the appellate court as to your opportunity to review any of the appellate file at the appellate court. But any review of the file will be for your interest only. The appellate process does not allow for any communications or participation in the decision on appeal by you.
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I'm curious as to why you want to review your trial testimony? And why you want to send a letter to the judge who presided over the trial? Why are you concerned about perjury? As the other attorneys have written, you are not entitled to a transcript of your trial testimony and any letter sent to the judge will not have any effect as the case is out of the judge's hands. The appellate court is bound by the evidence that was introduced at trial and cannot consider any other evidence.