You can't deal with a neighbor like that. I have been there, too many times. Eventually the HS will get sick of you calling and you'll be the "bad guy". Have them deliver the statute and message to the owner so it is on record.
NC Statute Chapter 67. Dogs. Article 1. Owner's Liability.
§ 67-1. Liability for injury to livestock or fowls
If any dog, not being at the time on the premises of the owner or person having charge thereof, shall kill or injure any livestock or fowls, the owner or person having such dog in charge shall be liable for damages sustained by the injury, killing, or maiming of any livestock, and costs of suit.
§ 67-3. Sheep-killing dogs to be killed
If any person owning or having any dog that kills sheep or other domestic animals, or that kills a human being, upon satisfactory evidence of the same being made before any judge of the district court in the county, and the owner duly notified thereof, shall refuse to kill it, and shall permit such dog to go at liberty, he shall be guilty of a Class 3 misdemeanor, and the dog may be killed by anyone if found going at large.