I'm surprised a lawyer on here recommended a demand letter- it's not worth it. They will not be held responsible by the law from what you wrote. The owner of the property is in real estate- they will know that. If a tree falls onto someone's house- that homeowner whose house it fell on is responsible for the repairs. Once the tree crossed onto your property, you had a right to cut it down, if you choose to. If you are looking for coverage, contact your homeowners insurance. Sorry, I know it's not what you want to hear, but hope it's helpful