Does the parent filing for statutory rape have to be in the same state as their child?

No, any crime can be reported to the appropriate law enforcement agency by anyone with knowledge, regardless of where they live. Of course there is no requirement that a parent of a child who has had sex with someone too old be the one to report it. Ultimately the State won't be able to prove it without the cooperation of the child or the admissions of the defendant, unless someone else saw them having sex. The parent usually doesn't have personal knowledge to testify at the trial.