well if he has dead trees on his property, I would call someone, so you don't have to deal with this again. But here it is also the responsibility of the person whose yard it falls in to clean it up.
I live in a house that is at least 125 yrs old - it was the original house on a huge farm that about 95 yrs ago was slowly sold off, so its all neighborhoods. But in my backyard is one of the oldest, biggest trees around probably closer to 200 yrs old. Anyhow, a few years ago, this guy buys the house next door to me & one day calls me on the phone - I'd never met him, which meant he had to have gone to the county assessor's website, found my name & looked me in the phone book.
He calls over telling me, your tree is hanging partially over my house & I want you to cut it down because there are limbs hanging over my bedroom and I don't want them to fall off & crash into my room & kill me
-- I told him I would do no such thing. He was so ignorant - he couldn''t see the hundreds of dollars he was going to save on air conditioning due to the tree shading his stucco house. I can go for weeks without ever turning my air on because of this tree & the stucco. He had no regard for the environment & the life of this tree or my personal property.
I told him, I would do no such thing, the tree is very much alive. I questioned him why he would have ever bought the house if he was so afraid of my tree. He was a jerk on so many other levels in the short time he owned the house. I was glad when he moved, although that house has been owned by a succession of royally idiotic people - now the people there have backed into my wooden fence & the only thing holding it up is the frozen ground & the little bit of twine I've strung around the fence & the posts. Would love to have them pay for the damage and repair - but I won't be holding my breath
So I know how bad neighbors can be.