I had that happen a few years ago when I was getting ready to sell my old house. A branch ended up nailing my detached garage. When I went over to inspect it, it was like out of a movie - every 5-10s another branch would come down somewhere in the neighborhood. In retrospect, it was probably really dumb to be outside at all that day.
Then, like out of a different movie, some of the shadiest dudes I've ever seen in my life started coming out of the woodwork offering to remove and cut up the branch. Thankfully my neighbor already had a legit business coming over to quote, so, I piggybacked on that. Since I was going to make an insurance claim, I wanted some more qualifications than: "has chainsaw".