S.C. Code Ann. § 5-3-100: Alternate method when entire area owned by annexing municipality or county.

If the territory proposed to be annexed belongs entirely to the municipality seeking its annexation and is adjacent thereto, the territory may be annexed by resolution of the governing body of the municipality. When the territory proposed to be annexed to the municipality belongs entirely to the county in which the municipality is located and is adjacent thereto, it may be annexed by resolution of the governing body of the municipality and the governing body of the county. Upon the adoption of the resolutions required by this section and the passage of an ordinance to that effect by the municipality, the annexation is complete.