After ice storm, tree fell on my car. Will my landlord be liable for the damage?

I rent a house. There is a pine tree that has been dying since before I moved in on the property. Two weeks ago we had a winter storm - freezing rain, below zero temps, wind gusts 30-40 mph. Well, this tree fell over and took out a couple fence panels and the top of the tree landed on my vehicle. It has... show more I rent a house. There is a pine tree that has been dying since before I moved in on the property. Two weeks ago we had a winter storm - freezing rain, below zero temps, wind gusts 30-40 mph. Well, this tree fell over and took out a couple fence panels and the top of the tree landed on my vehicle. It has produced 4 or 5 dings on the hood. My landlord had someone come over and chop up the tree and replace the fence panels. However, he is telling me that the vehicle repair he is not liable for because the tree wasn't dead, and there was no negligence on his part for not having the tree cut down to begin with. And that it will be my responsiblity to pay for the car repair. Is that true? Wouldn't he have insurance to cover it? Why did he repair the fence if he wasn't liable? BTW, landlord is also my insurance agent, so you see it's sticky!
Thanks for any insight you can provide me.
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