In normal play, you obey traffic laws, but a terrible AI driver runs a red light and crashes into you.
Other times, you find a stolen car or a car with a fake plate and intentionally run into it.
Either way, bumping or crashing into the car will cause the accident scene to start. Make sure not to crash too hard since excessive damage can prematurely end the shift.

Playlist

After the accident starts, the first thing to do is start taking pictures. This works similarly to regular accident scenes where you fill up the bar. The more you fill up the bar, the less points are deducted (a full green bar results in no cp loss).

After enough pictures are taken, you go up to the driver and apologize. This fills up the accident bar significantly. Once it is either in the extensive region (-5 points) or entirely green, you can either do an accident report or let them go.
After letting the driver go, you can stop them before they enter the car and cite them for expired ID. You can arrest for no license, fake plates/ID, stolen vehicle, warrants and stolen ID. You can't arrest or fine for DUI, no turn signal, no insurance, or other traffic violations. You also can not search the car even after an arrest; only tow.

If you can not justifiably arrest the driver, quickly assess the damage of the car. If it's heavily damaged (no plates, broken windshield, broken lights, etc.), tow the car. If the car has only minor damage and the info is clean, let the driver go. If they're drunk, carry invalid registration, invalid insurance, or commit other traffic violations, pull them over again.
After finishing the accident, go to the garage and do either manual repair or quick repair outside the garage.