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"I mean, I'm pretty sure the statute of limitations for the assassination of John F. Kennedy has already passed, so..."
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You know, actually, if you were to come up with the ability to go back in time, you could really have some fun by going back in time, killing, say, Andrew Jackson, then going forward well past any human lifetime and getting yourself thrown in jail for assassinating a president over 100 years prior. (Well, I say "fun". You'd be stuck in jail for assassinating a president. But it would make a fun story in a history book.)
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Okay, so I did some looking and it turns out there is no statute of limitations on presidential assassination, so if you were actually the one on the grassy knoll, I'd maybe keep that fact quiet and just keep pretending it was Oswald.