I am an attorney. Do not take this as creating an attorney-client relationship or as legal advice. However, here is my opinion, based on general principles of law. Note that the law may be different in the state where you live.
A dog owner’s duty is simply to not be negligent in the way in which the dog is kept. A dog kept in a yard with an adequate fence does not need to be leashed or otherwise further confined unless the yard is expected to be used by others on a regular basis, such as by a postal person or a meter reader. Even then, the dog does not necessarily need to be leashed or further confined if the owner has no reason to think that the dog is likely to bite someone.
If your neighbor was crossing your fence without your express of implied consent he was a trespasser. In a tradition going back to the time when people lived in caves, repelling trespassers was one of the purposes of dogs. Any animal behaviorist will tell you that it is not surprising that a dog would bite a trespasser, as the dog sees the act as a hostile invasion of the territory the dog is trying to protect. Which, by the way, it is.
So, you are probably not legally liable to the owner for the injury inflicted by your dog. Some areas of the country may view this differently, particularly if the dog is known to be a biter and no warning signs are posted. Whatever you do from here on out, it would be best to post a “Beware of Dog sign”.
As for calling the police, you are certainly within your rights if the neighbor is threatening to hurt your dog or actually trying to do so. Your dog is your personal property and this is no different than the situation where a neighbor threatens to take a baseball bat to your car or actually does so. As some posters have pointed out, though, there is some risk that the police might take the approach that your dog is dangerous and should be quarantined or even disposed of. On the facts stated, I do not think that is a big risk, but it is there. You cannot depend on the police to apply a very good legal analysis. They actually have very little training in the law, and many of them seem to have difficulty in understanding the concept of self help in defense of property. This is a general observation, of course, and I do not mean to say it applies to all police officers.
If this looks to be an ongoing problem you should consult an attorney in your area about getting a restraining order against your trespassing neighbor.