Tell him to do one.
If it's on your property there's nothing he can do. He can trim back the bits that cross the boundary line but that's about it.
I'd ask to see the problem, but I think it would a decision between you and your neighbour.
Edit - you're supposed to notify your insurers if you have a tree causing damage to a neighbouring property.
If he does trim the overhanging bits, he has to return those bits to the owner of the tree.
@JurekB started
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Tell him to do one.
If it's on your property there's nothing he can do. He can trim back the bits that cross the boundary line but that's about it.
I'd ask to see the problem, but I think it would a decision between you and your neighbour.
Edit - you're supposed to notify your insurers if you have a tree causing damage to a neighbouring property.