Legal Question in Family Law in North Carolina

If there is no custody order in place then yes she can. If she leaves and you find out about it, you can file an emergency custody petition to force her to bring the child back. Once the child has lived outside of NC for 6 months or more, NC will lose jurisdiction. If you are concerned, I would not wait until the mother leaves the state. Be proactive and file for custody/visitation now to get a court order established. If you can afford it, I suggest that you see a family law attorney.