I cut & pasted this from the NJ State Police website.
All firearms transported through the State of New Jersey:
The following guidelines are provided in order to assist law enforcement officers in applying New Jersey's firearms laws to persons who are transporting firearms through the State of New Jersey.
I.New Jersey laws governing firearms permits, purchaser identification cards, registration and licenses do not apply to a person who is transporting the firearm through this State if that person is transporting the firearm in a manner permitted by federal law, 18 U.S.C.A. 926A.
II.This federal law permitting interstate transportation of a firearm applies only if all of the following requirements are met:
The person's possession of the firearm was lawful in the state in which the journey began;
The person's possession of the firearm will be lawful in the state in which the journey will end;
The person is transporting the firearm for lawful purpose
The firearm is unloaded
The firearm is not directly accessible from the passenger compartment of the vehicle
The ammunition is not directly accessible from the passenger compartment of the vehicle
If the vehicle does not have a compartment separate from the passenger compartment, the firearm and ammunition must be in a locked container other than the vehicle's glove compartment or console;
The person is not
a convicted felon
a fugitive from justice an addict or unlawful user of drugs, or
an illegal alien
The person has not
been adjudicated to be a mental defective
been committed to a mental institution
been dishonorably discharged from the armed forces, or
renounced his United States Citizenship
III.A person who is transporting a firearm though the State of New Jersey in the manner permitted by person's possession 18 U.S.C.A. 926A, see Section II above, need not give notice.
IV.Procedures for Investigation of Conduct Involving the Possession or Transportation of Firearms
An officer who reasonably suspects that a person is transporting a firearm in violation of New Jersey law should make reasonable inquiries in order to confirm or dispel that suspicion.
In a case where circumstances reasonably indicate that the person's possession and transportation of the firearms my be permitted by 18 U.S.C.A. 926A, the officer should make reasonable inquiries in order to determine whether the person's possession is permitted by that federal law.
If reasonable inquiries lead an officer to conclude that the person's possession is lawful under either New Jersey law or 18 U.S.C.A. 926A, as described above in Section II, the officer should promptly allow the person to proceed.
Whenever an officer has probable cause to believe that a person's possession of a firearm is in violation of New Jersey law and not permitted by 18 U.S.C.A. 926A, as described above in Section II, then the officer should make an arrest.