Auto Insurance Claims: backed into in a private parking lot, own insurance, independent party

Question
I was backing into a spot in a private parking lot. when a car backed into the side of my vehicle.  The spot was on my side of the lane and the other driver was backing against the direction of her lane.  the police were called and took statements and said he could not assign fault with either one of us so no tickets were issued. I have her insurance numbers and need to know what to do.  She did not give me her agent's number so can I go to a local agent and file the claim against her or do I go through my own insurance agent and have them battle it out with her insurance. Or is it just a case of he said she said and it will end up my insurance pays for mine and hers for her car?

Answer
First report the claim to your insurance.  Then call her insurance if you think she owes for your damage.  Both sides will ask you to give a statement, probably recoded.  This is normal and I recommend you cooperate, as this will speed the process.

Both insurance claim reps will do their own investigation and each will make a determination regarding liability.  They may not agree.  They may decide one party is 100% liable, or they may decide each party was a certain percentage liable.  The laws of your state will be important in how this is assessed, because every state has different rules.

If the insurers do not agree, they will go to arbitration, where an independent party will decide.

These types of claims are very common and often the parties disagree as to who was liable.