If I am a non resident in South Carolina but sold a house there with $0 gain, do I need to file a state tax return there?

A nonresident individual receiving South Carolina income from wages, rental property, businesses, or other investments in South Carolina, must file an SC1040 South Carolina Individual Income Tax Return and Schedule NR Nonresident Schedule. 
 

See Code Sections 12-6-1720 and 12-6-2220.

SECTION 12-6-1720. Taxable income of nonresident individual, trust, estate, or beneficiary; modifications, adjustments, and allocations.

A nonresident individual, a nonresident trust, a nonresident estate, and a nonresident beneficiary shall report and compute South Carolina taxable income as a resident taxpayer of this State subject to the following modifications:

(1) South Carolina taxable income, gains, losses, or deductions include only amounts attributable to:

(a) the ownership of any interest in real or tangible personal property located in this State;

Also, it is quite possible that SC taxes were withheld at the time of sale - and you'd have to file an SC tax return to claim any refund you might be due.  Check your closing documents.

https://law.justia.com/codes/south-carolina/2012/title-12/chapter-8/section-12-8-580/

SC will receive the 1099 showing your sale,  but have no idea you had no gain, so you need to do a return to show that, when they do a match with the 1099, it will not generate a tax notice.