A partnership withholding income tax on your behalf is the same as an employer withholding tax. Withholding and filing are two different things. You have not filed a return unless you actually file a return.
South Carolina says: "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."
The penalties for non- or late filing and/or non- or late payment are based on unpaid tax. If you have withholding, you may not owe any SC tax, in which case SC will not care whether you file a return or not.
If you are using the online version of TurboTax you can prepare a nonresident return and see whether you owe. If you do not owe, you can delete the return and pay nothing for state.
If you owe a minimal amount, you can choose not to file. Generally states have a threshold where it is not worth their time and effort to collect small amounts of tax due. That does not mean you are forgiven for not filing.
However if you continue to receive SC income every year and have unpaid tax every year, at some point you will probably get audited and asked to file past returns and pay tax plus penalty and interest.
