Auto Insurance Claims: Auto Collision Claim Process, own insurance, auto collision

Question
I was recently involved in an auto accident where I was rear ended by another driver.  We pulled off to the side of the road and exchanged insurance and personal information.  She called a police officer and one arrived at the scene of the accident shortly after.  No police report was taken and no fault was claimed by either of us.  Am I in danger of losing out of her insurance covering the damage to my vehicle?  

I was told that when there is no police report or fault admitted that the two parties involved simply handle it themselves and have their own insurance companies fix the repairs for them.  

Can you clarify these processes for me please?

Answer
In general, any collision that occurs rearward of the rear axle of a car is considered the fault of the party that struck the car. This is true in every state I know of. If I were you, I'd file a claim under her liability coverage with her company and see what happens.

The police has to have made some report or started paperwork on the incident as a matter of routine. Contact the police department and request a copy of the officer's report of that incident.