There's two types of law you have to think about, Criminal and Civil. Criminally, I do not see a specific law prohibiting videotaping someone in your car (assuming the only activity going on in your car is driving- there are statutes on Voyeurism) .
Civilly, it probably depends on if the person feels an expectation of privacy, which is unanswered by case law. To avoid be a test subject on whether someone can sue you, it's safer to post a notice, just like you see when you enter any store with video surveillance. Of course then there is always the question of the adequacy and prominence of the notice.
If you ever have someone famous in your car, there might be restrictions on what you can do with that person's image, as it is seen as having monetary value.
If this post contains any legal opinions, it must not be considered legal advice. Legal advice is obtained from a lawyer that you have retained. These comments are provided for discussion only.