Trees do indeed fall and kill people. Contact a certified arborist and get the facts about your trees. Your tree might be dangerous or maybe not. But find out from a person trained in tree care. A neighbor is complaining about your tree or even speaking in threatening tones.
Some folks fear or hate trees.
They hate cleaning up after them or fear they will fall. Listen respectfully to your neighbor because they might have a well founded request. Call a certified arborist and get good, solid information about your tree's health. Don't guess or be swayed by emotion alone. If they are threatening a law suit call your lawyer and find out your rights.