Amends Section 2.02 of the Charter of the City of Conover set out in SL 1977-78, which provides that all extensions of the City's corporate boundaries are governed by general state law. Authorizes annexations without a referendum on the annexation ordinance required by law under GS 160A-58.55(i) (Referendum vote on annexation ordinance) and GS 160A-58.64 (Referendum prior to involuntary annexation ordinance) if the total area to be annexed is completely surrounded by the City's primary corporate limits. Specifies that the remaining provisions of Part 7, Article 4A, GS Chapter 160A (Annexations Initiated by Municipalities) apply to annexations authorized by the Section, as amended. Provides for property tax liability for real and personal property in the area annexed under the Section, as amended, to be governed by GS 160A-58.10 (Tax of newly annexed territory).