if your portion of the tree hit the house then its their tree unless the tree or limb is dead. i know it doesnt make sense, but believe me i know from experience.

during the last line of storms the neighbors big oak tree fell and landed on my house. 30 grand in damages and my insurance company said by law my insurance has to pay damages due to it being an act of nature due the storm. BUT that tree was damaged in the last storm and i have pictures of it, so my insurance company said they may sue the neighbors for the amount of repairs. also i have told those people that tree needs trimming but they said it would cost 700 bucks and they were going to let it fall and let the insurance pay for it. well, he could have used the money his wife spent running for public office(and lost badly) to trim the tree.

what i am going to do is work with the codes enforcer to see if there are any city codes that may apply to force people, i mean idiots, to cut their trees if they post risk to other peoples property.

on top of that part of their carport sits on my property that i found out the other day, and i am going to see if i can have them to remove it. then i am going to build a 10 foot privacy fence and place about 6 bird feeders on top of it and see house they like all the bird poop on their carport.

It wasn't "my portion" of the tree that hit their house. The tree splits the property line at its base, and then increasingly leans in their direction. It is all the way on the property by the time you get 20 feet up. The limb that fell, was clearly on their property.

So, if I am understanding you fully, I am not obligated to do anything unless the tree was dead or damages, which it was not. Though, still strange that it came down on a windless night....