My mother is cosigner on my vehicle and her insurance is saying she cant insure my car?

When insuring any vehicle it is important that the person trying to get insurance on the vehicle itself is either the full or partial owner. Since your mother is a partial owner of the vehicle that means that she meets this qualification for getting insurance under a policy. The 2nd step after that is finding a company that will create a policy where the person in question has partial ownership. There are a lot of insurance companies out there that would rather the person have full ownership in order to reduce the risk of insuring that person in the first place. Some companies will deny that person a policy just based on the fact that they are only a partial owner. Make sure that the company that you are attempting to get a policy from does not discriminate against partial owners when it comes to creating a policy. With regards to your state law question, yes under New Jersey law she should be allowed to place a vehicle that she has partial or full ownership under her existing policy as long as the company she is working with does not deny her a new policy based on the partial ownership. If the company in question does not allow her to, I suggest finding a new company that would insure the specific vehicle that you have in question.