What action can I take after being verbally threatened?

You can go to the police and report it.  If they're unresponsive, go to a magistrate, and swear out a complaint.

There are various possible crimes here.  If the threat was accompanied by some physical jesture or physical movement, the person may be convicted of some sort of assault.  In all likelihood this is a simple assault, a Class 2 misdemeanor, since it seems that no physical touching took place that resulted in injury.  If a weapon - a bat, gun, knife etc. - was involved, the crime might be more serious.

In addition, North Carolina has the crime of "communicating threats" which is a Class 1 misdemeanor, slightly more serious than simple assault.  In order for someone to be convicted of communicating threats, the verbal or written threat needs to be communicated so that both a reasonable person would believe that the threat would be carried out, and the person being threatened feared it would be carried out.