Do I need to file a tax return for SC if I have rental income in the state, but was a nonresident for the whole year?

Yes, you will need to file a nonresident South Carolina income tax return if you had rental income from property in South Carolina.  See Code Section 12-6-2220.

Thanks, do I still need to file tax returns for SC if the my tax due is $0 for SC?

If there is no taxable income, you do not have to file the South Carolina tax return.  @ningzhu60 

Thanks again. Continuing from the previous question, do I get tax refunds on my SC rental income after I file my NH tax return (since there’s no tax on income and rental income in NH)?

No, there would not be any tax refunds available for your South Carolina rental income.  There would also not be any tax credits available since the income isn't taxable in more than one state.