Can I claim some part of damages from the parking authorities

I own a Maruti Ritz which is parked in a Government Authorized parking lot. I pay monthly fee of Rs. 1800 every month. Just on the night of 30th Dec when the vehicle was parked in the parking lot, I was informed that windshield of vehicle of car got totally damaged by fallen tree. The parking associates told me that it was because of monkeys which shook the tree which fell on the ground. I went ahead and logged a Police Report ( NOT FIR). I now have the copy of report with me. Unfortunately, the car insurance got expired on 25th Dec whereas the accident took place on 30th ( as told by associates but which is pending investigation , validation and confirmation by police). My question is , can I claim some part of damages from the parking authorities which happen to be Jammu Development Authority, J & K in this case. Since, they had the ownership of my vehicle they should pay part of damages is my view. I would like to get your legal opinion.