yes - if this a paper filing?
what LA would want to see is that the tax credit they are giving you matches the tax liability on the SC tax return.
Q. Can you submit another state form to your home state for verification of filing?
A. Yes. Most states require that you attach a copy of the other state return, when claiming a credit (on your home state) for tax paid to another state. If e-filing you home state, thru TurboTax (TT), TT will automatically include a copy of the non resident state return. When filing by mail, you should attach a copy.
They did not submit one last year from SC to our Louisiana (home state) for a job we worked in SC. So you probably ought to make sure that this is really done. I had to send supplemental info to Louisiana last year to prove we filed in SC. We ended paying $49 for the extra SC form (which is a bear of a form to do) for a $78 dollar refund for a 3 day job that we made maybe $500 on. In long run, it was not worth it!!!