The Notice of Appeal to the Supreme Court has to be filed within 15 days of the date the mandate issues from the Court of Appeals. The Court of Appeals issues its opinion on a certain day, but the opinion is not completely official until there is a "mandate" which occurs many days later. According to the NC Appellate Court's website, for NC Court of Appeals opinions that came out on December 4, the mandate will issue on December 27, 2012. So, you have 15 days from that day to file the Notice of Appeal. But, it is usually a good idea to not wait until the last day in case there is a problem with date calculation. I would advise filing the Notice of Appeal as soon as possible after the mandate issues. This is not something that you should try to do on your own. There are too many deadlines and certain things that have to be done in a certain order and if you miss one then you are finished. Since you had a dissent in the Court of Appeals, you have an appeal as of right to the Supreme Court and you don't want to waste that by missing a deadline.
Legal disclaimer: Rebecca Watts is licensed only in the state of North Carolina. This response does not constitute legal advice and does not create an attorney-client relationship. This response is only intended to provide general information and there may be other facts relevant to the issue which were not disclosed by the questioner and which would affect the answer. For specific legal guidance, the questioner should confer with an attorney about the specifics of his or her matter.