S.C. Code § 31-3-400
In addition to its other powers, a housing authority created for a city may exercise any or all of its powers within the territorial boundaries of any other municipality not included in the territorial jurisdiction of such housing authority for the purpose of planning, undertaking, financing, constructing and operating a housing project within such municipality, if a resolution shall have been adopted (a) by the council of such municipality in which the authority is to exercise its powers and (b) by the housing authority of such municipality, if one has been theretofore established by such municipality, declaring that there is a need for the housing authority of the aforesaid city to exercise its powers within such municipality.
S.C. Code § 31-3-400