N.C. Gen. Stat. § 160A-104
The people may initiate a referendum on proposed charter amendments. An initiative petition shall bear the signatures and resident addresses of a number of qualified voters of the city equal to at least ten percent (10%) 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 petition shall set forth the proposed amendments by describing them briefly but completely and with reference to the pertinent provisions of G.S.160A-101, but it need not contain the precise text of the charter amendments necessary to implement the proposed changes. The petition may not propose changes in the alternative, or more than one integrated set of charter amendments. Upon receipt of a valid initiative petition, the council shall call a special election on the question of adopting the charter amendments proposed therein, and shall give public notice thereof in accordance with G.S.163-287. The date of the special election shall be fixed on a date permitted by G.S.163-287. If a majority of the votes cast in the special election shall be in favor of the proposed changes, the council shall adopt an ordinance amending the charter to put them into effect. Such an ordinance shall not be subject to a referendum petition. No initiative petition may be filed (i) between the time the council initiates proceedings under G.S.160A-102 by publishing a notice of hearing on proposed charter amendments and the time proceeding under that section have been carried to a conclusion either through adoption or rejection of a proposed ordinance or lapse of time, nor (ii) within one year and six months following the effective date of an ordinance amending the city charter pursuant to this Article, nor (iii) within one year and six months following the date of any election on charter amendments that were defeated by the voters.
The restrictions imposed by this section on filing initiative petitions shall apply only to petitions concerning the same subject matter. For example, pendency of council action on amendments concerning the method of electing the council shall not preclude an initiative petition on adoption of the council-manager form of government.
Nothing in this section shall be construed to prohibit the submission of more than one proposition for charter amendments on the same ballot so long as no proposition offers a different plan under the same option as another proposition on the same ballot.
N.C. Gen. Stat. § 160A-104