Yes. The Department of Revenue recovers debt owed to the State of Iowa, including court debt, using income tax offsets through the Income Tax and Vender Offset Program. If your tax refund is being held due to outstanding court debt, you will receive a notice from the Department of Revenue. If you receive a tax offset notice, the amount withheld was paid to the judicial branch and you should not pay that amount towards your debt.
There are other state and county entities that can withhold owed fees from your state income tax refund.