Probably not. You probably do not have to file a SC return. As you state, you don't have SC tax due because any gain from the sale of home is being excluded from taxable income.
Although you do not have to file a SC return, you still may choose to do so just so that SC also has a record of you reporting the sale and the exclusion of gain so that they don't ask you questions. But you are probably not required to file a SC return.
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