Who bears the responsibility in a hypotethical scenario when a self-driving rideshare vehicle, without a human driver, god-forbid, hits a pedestrian?
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.
I would argue that new laws are absolutely needed.
USA laws are more directed towards helping companies and hurting individuals. Example of bankruptcy is a good one. Companies can shed more liability where individuals retain it after bankruptcy.
Civil liability is only viable if one has the funds to take action. This creates a David vs Goliath scenario were Goliath has an army behind them. Only method to remedy this would to change / pass a law that the party which loses must pain all court costs. It creates a level playing field for actual action against big business. I believe the UK has something like this in place.
Criminal liability is a joke when it comes to big business. They will bake the cost of fines as the cost of doing business. Make $1,000,000 braking the law and only pay a $1,000 fine results in $999,000 profit. Something like three strikes and the CEO, top executives, and three primary share holders go to jail while forcing the company to dissolve seems to be the only solution to removing bad actors in corporate settings.
Our current laws protect corporations and bad actors, with-in them, while harming the victims.