A Pop and a Crash

So the other night I was sitting in my living room with the back door open to let in some fresh air, and I hear a strange popping noise. I listen, the dog perks up and stares at the door...but nothing else happens. So I go back to what I'm doing, only to be startled by more popping. Finally I get up and shut the door, unnerved at not knowing what the strange sound is. As soon as I sit back down on the couch I hear what sounds like oddly muffled thunder...just over my house. One glance out the back window reveals all: A large branch from the neighbour's tree had broken from the trunk and landed partially on our roof and partly in our yard. It's still partially attached to the trunk, I think. I'm still not sure what to do about this...