From and after July 1, 1997, whenever any statute requiring the remittance of an excise or income tax prescribes a due date therefor, such due date shall be deemed to be complied with, and no penalties shall be imposed for late payment, if such payment is mailed on the statutorily prescribed due date as reflected by the postmark on the envelope containing the payment. The use of private delivery services shall be allowed by the secretary of revenue, and the determination of timely filing regarding such services shall be made, in the same manner and to the same extent as provided by section 7502 of the federal internal revenue code of 1986, as in effect on September 1, 1996.