If your efforts at working something out with your neighbor haven't succeeded, talk to the animal control department in your city or county. The people there are likely to be more receptive than the police or other municipal officials.
When you call, don't just make your complaint and hang up. If it's really a persistent problem, you need to be persistent, too. Find out how to follow up and get results. Ask the person you talk to—and write down his name, so you won't have to explain your problem every time you call—about the department's procedures. Find out what the department will do, and when. For example, if the problem is a barking dog, the department may need to receive a certain number of complaints within a certain time before it will act. If that's the case, you may want to discuss the problem with neighbors; if they feel as you do, enlist their help.
Some cities have set up special programs to handle dog complaints. The animal control department establishes a simple procedure for making a complaint, and follows up promptly—and repeatedly, if necessary. This is a great idea, for two main reasons. First, it gives a specific city official or department—usually the health, police, or public safety department—responsibility for the problem. Otherwise, if it's not clear who's primarily responsible, someone with a complaint is likely to get shuffled from department to department, explaining the problem to six different people during each call.
A dog complaint program also lets everyone—dog owners and their neighbors—know what they can expect. A predictable system of warnings and sanctions tells dog owners what's expected of them and lets neighbors know what it will take to solve a problem before it drives everyone in the neighborhood batty. Of course, it doesn't do much good unless these rules are published and readily available—which, unfortunately, is rare.