My Oklahoma state taxes were accepted but when I check status of refund it says "a refund is not due" What does this mean?

If your OK return made by TurboTax showed a refund and it is was accepted, but the state website says that a refund is not due - you will have to contact the taxing authority in Oklahoma - TurboTax has no control over your return once it is sent to the taxing authority and accepted.