Subject to the approval of the registered voters of Oak Island in a referendum conducted on November 8, 2011, adds a new Section 5.4 to the town charter providing for the recall of the mayor or any member of the Town Council (Council). Allows a recall petition committee, comprised of at least five members who are registered voters within the town, to file an affidavit with the Brunswick County Director of Elections (Director) naming the individual for which removal is sought and the grounds for removal. Sets requirements for petition forms to be provided by the Director upon the filing of an affidavit and provides for recordation of the petition. Requires that the petition be signed by at least 25% of the town’s registered voters and that the petition be returned to the Board of Elections (Board) within 30 days of filing of an affidavit. Establishes the process to be followed by the Board in investigating the sufficiency of a petition and allows amending a petition upon a finding that the petition is insufficient. Requires an officer to resign within five days if it is determined the recall petition is sufficient; if the official does not resign, requires the Council to order and fix a date for a recall election. Provides for the scheduling and notice of the recall election. Also provides for filling the vacancy when the official does resign. Provides that if less than a majority of the votes in the recall election are for recall, then the official continues in office for the remainder of the term; if a majority of the votes are for recall, the official is deemed removed from office on the date that the Board certifies the results. Provides guidelines for a recall petition against an official who has already been the subject of a recall petition and for the recall of two or more members of the Council (or the Mayor and one or more members of the Council).