Do I have to cut it down

So my neighbor emailed me pretty much telling me I have to cut a tree down. So it looks like half of the tree did break and is leaning in my yard and I’m OK with that. He’s saying that the tree fell on his leaning on some branches on his property, which is false. He has no trees on that side of the property, he pretty much wants me to cut it down before it falls. On that side of his house, there’s nothing that would get damaged if the tree did fall, he has about 4 acres and our property lines nowhere near his house or structures or anywhere where there’s people. Legally, do I need to cut it? We’ve had some beef in the past, although we’ve only been there for a year with trees and landscapers and such so I really don’t wanna cut it.