The New Jersey Self-Reporting Crash form (SR-1) is used to report a crash that was notinvestigated by the police and it is the only form that can be used for this purpose.
The electronic versions below enable NJ citizens to fill out a form online and receive acknowledgment back within minutes. The online receipts are equivalent to the paper versions stamped by the NJDOT and can be submitted to an insurance company. (From the NJ DOT website)