I would say health insurance. And before if not, then maybe home owners or renters insurance. Car insurance would be the least likely.
Most policies say that the injury has to arise from the "use, maintenance or operation" of the vehicle. If the way you were injured falls under any of those, your auto medical or No Fault should apply. If you just happened to be injured while sitting in the car (one example,a person burned themselves with a cigarette), then health should apply
I work for a healthcare subrogation company so I deal with this all the time. Technically, under some auto policies, they can be responsible for injuries related to your vehicle even if it's not running and in your driveway (ex. loading/unloading, getting in/out, working on it, etc.). If that's not the case, the health insurance would be responsible.