Renter's insurance is the common name given to an HO-4 homeowner's insurance policy. The coverage renter's insurance provides is almost identical to the the coverage offered by most standard homeowner's policies, including provisions for a fallen tree. The big difference between renter's insurance and homeowner's insurance is coverage of the physical structure. Your renter's policy won't cover that. Instead, your landlord's insurance policy should pay for structural damage.
Renter's insurance covers you against loss of your personal property, so if a wind storm blows a tree down on your apartment and smashes your TV, the damage to your television is covered. Your renter's policy will cover water damage to your belongings caused by rain that entered your home due to the tree crashing through. Your personal property includes the stuff you own, such as your furniture, clothing, appliances, electronics and utensils. If you have valuable personal property, such as jewelry or expensive musical instruments, you might need to add a rider to your policy to cover their loss.
Your renter's insurance policy comes with a minimal, no-fault medical payments provision that typically covers form $1,000 to $5,000 of medical expenses. If that tree injured someone other than a family member when it crashed into your apartment, that person could submit her medical bills to your insurance company. The liability portion of your renter's policy will also pay to defend you in court if you get sued because of damages caused by the fallen tree.
Additional Living Expenses
If the fallen tree caused sufficient damage to render your abode unlivable, your renter's insurance will help pick up the tab for costs associated with the resulting extraordinary living expenses. While you are waiting for your home to be put back into habitable condition, the additional living expenses portion of your renter's policy will typically cover the difference between your ordinary living expense and what it costs for temporary lodging, eating out and other extraordinary expenses.
Expenses Not Covered
Your renter's insurance policy typically has a "no harm, no foul" provision. If a tree falls on your rental property, but doesn't cause any damage, the policy won't kick in. It won't pay to have the fallen tree removed. That will be at your expense. It also won't pay to trim or remove a potentially dangerous tree. That's considered a maintenance issue, one you or your landlord will have to deal with.