We have to watch out for Terminology here; You get notice that your "Tax Return" was accepted
"Tax return" Means your tax filing and it's data. So a tax return is what you send to the tax authorities (federal, state or municipality).
People misuse the term "Tax Return" to mean "Tax Refund"....but they shouldn't.
A tax return is what you file. Whether you owe more taxes (balance due) or whether you are supposed to get a "refund" is shown in that tax return data.
So if your state tax filing (Tax Return) indicates you need to pay the state some more money, then that $$ amount is what you need to send them.
Usually you send them a check with a tax voucher that is in your state printout, or go to your state's website to arrange payment, or "some" states allow payment to be arranged as a part of your tax return filing.
____________*Answers are correct to the best of my knowledge when posted, but should not be considered to be legal or official tax advice.*
