With all of the recent storms in Ohio I am often asked about damage to homes due to trees falling or large limbs hitting homes or autos.
My answer is usually "it's complicated."
If your neighbor's tree falls on your house or car, who pays? Depends. If the owner knew the tree was dead and did nothing, then they would likely be responsible. If the tree was live and hit your house then your insurance would handle it. They may elect to recover from the owner's company.
If your tree is partially uprooted but no damage was caused your company will probably not cover it. Get it taken care of immediately to avoid loss or injury.
If your tree hits your car? Not generally a homeowner's policy issue. File a claim under your auto policy for your comprehensive coverage.
As always, consult your agent. They live where you live. The 800#'s can be talking to you from anywhere in the world and the answers may not always be consistent or accurate..