You do have some recourse, however. Since you imply the letter was forged, you can hire a handwriting expert (not terribly expensive, by the way) to prove the signature is forged. At that point, you can then file charges for false arrest (if an arrest was affected), or filing a false police report (that one might be a joint accusation to both the principal and the 5th grader.)
Just the way the note was written would be a stupid way for a person to write a note - signing a name to a murder threat and just to make sure you could be found, saying what grade you were in. Having four officers there for something like that doesn’t make sense to me. The whole thing just seems stupid - like they should have known it was a set-up.