S.C. Code § 31-3-750
The territorial jurisdiction of a housing authority of a county shall be coterminous with the boundaries of the county in which such authority is situated but shall not include that portion of the county within the territorial jurisdiction of any housing authority of a city. But notwithstanding the provisions of this section the director may extend the territorial jurisdiction of a housing authority of a city over territory contiguous thereto, including territory included within the territorial jurisdiction of the housing authority of a county, and such extension of the territorial jurisdiction of a housing authority of a city and limitation of the territorial jurisdiction of the housing authority of the county affected thereby shall not be deemed to conflict with the housing authority of the county within the meaning of Section 31-3-390 unless a housing project shall have been constructed or acquired or the director shall determine that such a project is about to be constructed or acquired by the housing authority of such county within the territory proposed to be included within the territorial jurisdiction of the housing authority of the city.
S.C. Code § 31-3-750