S.C. Code Ann. § 16-5-40: Duty of officers to execute warrants.

All sheriffs, constables, and other officers specially empowered shall obey and execute all warrants and other processes issued under the provisions of Sections 16-5-10, 16-5-20, or 16-5-50 and directed to them. If a sheriff, constable, or other officer specially empowered refuses to receive a warrant or other process when tendered to him or neglects or refuses to execute the same, he is guilty of a misdemeanor and, upon conviction, must be fined five hundred dollars or imprisoned not more than three years. Fines collected are for use of citizens deprived of the rights secured by the provisions of this chapter.

Warrants and other processes run with and are executed by officers anywhere within the circuit or county in which they are issued.