Im not a game warden but i can help u out because i had the same question a few months ago and emailed a nc game warden. The law states you can hunt coyotes on public land aslong as there is another game season open, for example if small game season is in you can hunt yotes, or during turkey season or deer season. However there are a few stipulations one is that you can only use a weapon that is legal for the game that is in season. Examle...during turkey season you are limited to a shotgun, however during small game season in jan and feb you can use a centerfire rifle bcuz bobcat is in season until end of feb. Also you are npt permitted to hunt at night or on sundays like you can on private land. I know this post is a little old but hopefully it helps you interpret the law bcuz our regulation digest is not very clear on this issue.
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