I've lived in the US my entire life and have traveled extensively to all but 3 of the states. I know of NO state where it is not legal to own a video camera. I have checked the laws to try and find one where this is true, and have found nothing (except for a few states where it is not legal to have white lights on underwater video cameras, but that's only because it is not legal to fish using submerged white lights).
I don't know where you heard that, but if you could back up your claim with a little proof, or even which state, I'd appreciate it. I definitely do not want to get busted because I have a video camera with me.