N.C. Gen. Stat. § 160A-103

An ordinance adopted under G.S. 160A-102 that is not made effective upon approval by a vote of the people shall be subject to a referendum petition. Upon receipt of a referendum petition bearing the signatures and residence addresses of a number of qualified voters of the city equal to at least 10 percent of the whole number of voters who are registered to vote in city elections according to the most recent figures certified by the State Board of Elections or 5,000, whichever is less, the council shall submit an ordinance adopted under G.S. 160A-102 to a vote of the people. The date of the special election shall be fixed on a date permitted by G.S. 163-287. A referendum petition shall be addressed to the council and shall identify the ordinance to be submitted to a vote. A referendum petition must be filed with the city clerk not later than 30 days after publication of the notice of adoption of the ordinance.