Not in Virginia that I know of. Virginia also doesn't have a duty to retreat, i.e. the equivalent of stand your ground.I doubt Chris could even AFFORD a katana and even he has to be smart enough to know you can't carry a sword with you everywhere you go.....
Then again the Bat is already a legal grey area. I keep one in my car, but I make damn sure to have a glove and a ball in there as well as a cover story for law enforcement
People can and will tell you keep it off their property, though, and if you brandish it and threaten someone with it, the most likely thing Chris would do, you're also in deep shit. The circumstances under which you're carrying it, though, such as if you're driving to a riot with a car full of weapons, can show you have illegal intent.
You also can openly carry around a sword in a lot of places.
For an automobile, I'd say you're best with a tire iron or a MagLite or something that actually has some legitimate non-melee use. You want to be able to say plausibly that you weren't out looking for trouble, but that this was just the closest thing when a self-defense situation arose.
(Correct me if I'm wrong, there may be some specific locations where Chris is actually breaking the law with that bat, but I'm not aware of it. They won't let you into a courtroom with it and a lot of businesses will ask you to leave and, quite possibly, not to come back any more.)