Auto Insurance Claims: Accident - no police report filed, fender bender, insurance adjuster

Question
`Recently,  I was involved in a fender bender whereby the other vehicle hit me as I was preparing to park.  We exchanged insurance information and waited for the police.  We waited 2 hrs and the other party said they wanted to leave.  Nobody was injured and agreed to leave the scene on the assumption that we would not file a claim given the minimal damage.   However,  yesterday the other parties insurance adjuster contacted me and wants to hear my side of the story.  I personally have not contacted my own insurance and am wondering if I ought to contact my insurance or call back the other person's adjuster.  

What's is the best approach I should take?

Answer
Depending on the cost of repairs the other vehicle will require, the choice is yours. You might want to inform your insurance company if the estimate appears more than you are willing to pay out of pocket. Apparently the other party decided to use his insurance when he learned of the cost of repairs.