Here's a situation in which you can be a very good neighbor. Have the trees inspected by a Certified Arborist as soon as you can. This accomplishes two things: It shows respect for your concerned neighbors, and it identifies whether there is really a problem to be concerned about. 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 report 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.