Former patrolman here-
Every state and even locality is different as far as what the police will do for a minor crash. If you don’t regularly get in crashes and aren’t an expert on your state laws and local police department’s policies, call the police (non-emergency number) and have them tell you whether they will do a crash report, an information exchange, or nothing at all. Don’t be in a hurry. Wherever you were just headed… you’re going to be late, or you’re just not going to make it.
If there are any injuries, including just pain, call 911. If you are the one in pain, tell the officer, “I AM INJURED.” You can tell him that you do not want an ambulance (if you don’t), but if he says he has to call one because you said you are injured, don’t argue. When the ambulance gets to you, explain that you just have pain, but you do not need a ride to the hospital (unless you do). They will not take you against your will if you have no visible injuries and aren’t showing any signs of concussion or other head/internal trauma. [personal opinion - Don’t tie up the ambulance by making them take you to the hospital if you can get there safely yourself or by getting a ride from family/friends. Ambulances are a finite resource and any ambulance transporting someone with neck pain can’t save the life of someone having a heart attack.]
If you are normally comfortable just exchanging information and don’t feel the need to involve the police, that is fine, but be sure you are getting enough legit information from the other driver. If you try and call the police later because the driver gave you BS info, you might be out of luck because you didn’t call right after the accident. If the other driver is acting weird about giving you info, call 911 and tell the dispatcher that.
Don’t call your insurance company until after the ink on the police officer’s note pad dries. And don’t hand him the phone and tell him, “it’s my insurance company, they want to talk to you.” No they don’t. Not yet anyway.
And last but not least - PULL YOUR CAR OUT OF THE TRAVEL LANES!!!
If you have any car crash questions for a former police officer that used to handle a couple crashes a week (I am by no means an expert, but I’ve seen my share of weird situations working in an urban environment), feel free to ask them and I will do my best to answer.