Can you register a car in New Jersey if you have a Connecticut license?

don't think you need an NJ license but the NJ laws are so weird they may require it. In general you need to meet their 6 point system - if you go on the NJ dmv website you'll find what you need for the 6 points. Passport, utility bill showing residency, etc., they require points in different categories, if you have all that you may be ok.