Iowa Code § 423.47

If it shall appear that, as a result of mistake, an amount of tax, penalty, or interest has been paid which was not due under the provisions of this chapter, such amount shall be credited against any tax due, or to become due, on the books of the department from the person who made the erroneous payment, or such amount shall be refunded to such person by the department. A claim for refund or credit that has not been filed with the department within three years after the tax payment for which a refund or credit is claimed became due, or one year after such tax payment was made, whichever time is the later, shall not be allowed by the director.