Your Questions About Landlord Property Insurance Coverage

What are landlord responsibilities?

I have a property, who is rented by a tenant. A few weeks ago the water heater exploded and caused a flood. The tenant DOES NOT have renters insurance. As soon as she called me with the news, I called my house insurance provider to take action. They supplied a cleaning crew to get there ASAP to tear up the carpet and make repairs. The repairs will take a few months. Anyway the tenant is upset that there posessions are ruined. Such as couches, microwave, clothes ETC. She feels that I should reimburse her for the damaged to her personal property. I said the house insurance only provides coverage for the house not the possessions. Am I am responsible in any way shape or form? The cleaning crew has been there getting things prepared. They have ripped up the carpet, sprayed for mildew issue. They say its gonna be a step by step process. Eventually new carpet, doors and walls will be replaced.

Can she take legal action against me even though I have a cleaning and fix up crew there?
Is there a law saying that I have to pay money to my tenant for her loss of her possessions? Because she didnt have rental insurance.

Would a homeowner be responsible for car damage on his property?

I rent an apartment in Connecticut that is part of an old house that has been converted into apartment units. Through no fault of mine, a tree on the property fell and shattered the windshield.

My question is this: Would my landlord be required to cover the damages under some kind of homeowner's insurance, since the damage occured on his property through no fault of mine? I don't have glass coverage with my insurance, so it would be an out of pocket expense for me, but I believe that his insurance should cover it. Am I wrong?
I rent an apartment in Connecticut that is part of an old house that has been converted into apartment units. Through no fault of mine, a tree on the property fell and shattered the windshield.

My question is this: Would my landlord be required to cover the damages under some kind of homeowner's insurance, since the damage occured on his property through no fault of mine? I don't have glass coverage with my insurance, so it would be an out of pocket expense for me, but I believe that his insurance should cover it. Am I wrong?

ADDED DETAILS: The base and limbs of the fallen tree were completely rotted through, covered with mold and fungus. Does this make a difference?