The first thing you need to do is look at what the complaints have been.
You mention they have called both the police and animal control. Do you have a problem that you are not addressing?
If you live in pretty much any city there are animal codes. If you have a dog is it kept restrained to your property? Does it bark, as someone else mentioned?
In most cities it is classified as a nuisance if it barks for more than 30 seconds without stopping. Most cities also have strict leash laws that allow a leash of a specific maximum length, usually 6-8'.
Before you blame your neighbor make sure that they aren't in the right.
If the police come to your home on a complaint they are not supposed to say who complained, but they are required to tell you specifically what the complaint is.
If it is a complaint about your dog they are supposed to tell you what the dog is supposedly doing.
If you can honestly say that nothing is wrong on your end, and the police can't find any problem when they come, all you can do is attempt to talk to your neighbor in a non-confrontational manor. Be the better person. If they insist on continuing the problem file a harassment complaint with the police, if it is extreme look into a restraining order.