I have looked and looked and cannot find any leash law for Burlington, NC.  Our very sweet black lab loves all animals and tries runs up tail wagging even to the cat next door.  Needless to say the cat is not interested but we have seen the 2 interact, no problems.  No aggression is involved.   Another neighbor has 2 cats that we see at times wandering into our yard and as is the nature of a good hunting dog, our lab likes to follow their scent as she did last Saturday.  One cat went scampering up his tree and the neighbor went ballistic.   She was very rude to my son who was out with our dog and threatened with all sorts of legal action because of the "leash laws."    She says cats don’t have leash laws so her cats could come on our yard.   

Am I crazy or is that not right?  Please advise

Most pet control laws are in city or county ordinances.  Usually the easiest way to get information about local ordinances is to contact your local animal control agency.

Alamance County has an animal control ordinance.  It prohibits dogs that have been declared dangerous, potentially dangerous or public nuisances from running at large off the owner's property.  No leash is required, but the dog must be under the control of the owner.  If your dog has not been declared dangerous or a nuisance then it is not illegal for it to be at large. A separate state law prohibits dogs over six months old from running at large at night.

To see if Burlington has a leash law, call the Animal Services Center.

As a matter of being a good neighbor, you might consider taking steps to keep your dog out of other peoples' yards if they object.  I have three dogs and have fenced them in for their own safety.