S.C. Code Ann. § 7-13-2220

If any primary election, other than a nonpartisan municipal primary election, results in a tie vote and no candidate withdraws, the party officials shall conduct a runoff election to break the tie two weeks following that election. In the tie-breaking election, the laws of this State apply, mutatis mutandi. If the date for the tie-breaking runoff election falls on a legal holiday, it must be held on the same day of the first week following which is not a legal holiday. If a tie-breaking runoff election is required, any remaining primary elections required are postponed for two weeks. If the date for a postponed election falls on a legal holiday, it must be set for the same day of the first week following which is not a legal holiday.