If one of your neighbors expresses worry about a tree on your property, consider it a situation in which you can be a good neighbor. Have the tree(s) inspected by a Certified Arborist as soon as you can. This accomplishes two things: It shows respect for your neighbors, and it identifies whether there is really a problem that needs to be addressed. Your neighbors might have done you a giant favor by alerting you to a potential hazard! You might want to invite them to be there when the arborist comes, but in any case, it would be a good idea to share the arborist’s findings with them.
Take action on the arborist's recommendations. If a tree needs to be removed, get some estimates and get it done. You can be held responsible for damages to your neighbor’s property if you fail to remove a dangerous tree..