If an out of state driver with no auto insurance has an accident in NJ is their health insurance or the NJ driver's auto insurance primary?


Someone's health insurance is not going to cover any injuries in an auto accident. That covered by the insurance on the vehicle. Since there wasn't any, it would appear the victim(s) only recourse would be to sue. And hope they can collect any judgment they might be awarded.  
Health Insurance WILL most definitely cover injuries resulting from an automobile accident. Some motoe vehicle insurance policies even have a "health insurance primary" option. The questions was how to determine which is primary , the health insurance or the insured drivers motor vehicle coverage