Some states have autonomous vehicle statutes and some don't.

Let's assume the case none of them do, since it sounds like you are asking about "what would happen in the case this isn't specifically answered by a statute".

In that case, the short answer is:

Criminal liability - you could only really charge crimes that don't require specific intent. Reckless driving is an example. You could charge the company since they are the operator and the car is simply an instrumentality. In the end though, there just isn't a lot of people here with legally culpable conduct.

Civil liability - the company pretty clearly because civil liability often does not require the same kind of intent crimes do.

This is, of course, why states where autonomous vehicles operate have autonomous vehicle statutes :)

As a general rule, criminal law mirrors what society overall wants to decide is culpable/not, and the lag time isn't as bad as most people often think. That doesn't mean nobody ever gets hurt or dead without someone being as culpable as society wants, they do, and it often leads to a law with a name - megan's law, etc.

Criminal law is mostly reactive though, not proactive, and to be honest, proactive attempts don't have a high hit rate.