Are we liable for the auto deductible when we were hit from behind and the other driver left the scene of the accident. We have the police report stating this to be true.?

It depends on the state you live in but as far as I know if you are involved in a hit and run and you are NOT At Fault, the insurance will more than likely waive the deductible. Make sure you have a "COLLISION DEDUCTIBLE WAIVER" clause somewhere listed on your policy, usually it's included with full coverage policies.