car hit by fallen tree limb

My car was hit by fallen tree limb while parked in apartment parking lot. I want to hold the landlord responsible for this. I called my insurance company, the claim agent told me if the tree is alive then the landlord is not responsible for neglegence of maintenance. is this ture?
dos anybody have any experience in cases like this? any advise on how to deal with the landlord?
any advise will be greatly appreciated.