No way to know at this stage.
Might be a couple months before the state computers notice the overpayment.
________________
What likely happened was that the state filed a lien with the IRS to collect your past-due taxes from any Federal refund they see....thus the Feds did so because they are completely unaware that the state is also doing so with your state refund.
BUT, it may take a few months for the Feds to actually transfer those offset funds to your state, so the state doesn't know you've overpaid ....yet..
Yep...a bureaucratic/computer matching nightmare, and not much anyone can do about it at this stage.
____________*Answers are correct to the best of my knowledge when posted, but should not be considered to be legal or official tax advice.*
