Whilst with reference to trees, medical doctors think that the buildings insurance will cover damage which result from falling foliage. Yes they will - if the tree was well serviced. But what happens if the tree was rotten or already damaged? Yep, you've guessed - http://www.Shewrites.com/main/search/search?q=guessed it, that is the maintenance trouble. You're liable! Unless you can demonstrate that you took reasonable proper care of the trees, the insurer can refuse any subsequent claim. If have big trees one could have big complications.