S.C. Code Ann. § 5-15-125: Municipal elections resulting in tie.

If any municipal election results in a tie, the municipal election commission or the municipal party committee shall conduct a runoff election to break the tie two weeks following that election. In the tie-breaking runoff, 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 set for the same day of the first week following which is not a legal holiday. If a tie-breaking runoff election is required, any remaining municipal elections required are postponed for two weeks. If the date of 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.