I was wrongfully accused of a hit and run, how long does the "victim" have to report to the police?

The victim can report at any time, but the longer they do, the harder (if not nearly impossible) it will be to prove the case, decreasing the chance that anything will get filed by the DA.

Assuming it's a hit and run with property damage only (a misdemeanor), then the statute of limitations for the DA to file is a year.