Whenever the tax administrator determines that any person is entitled to a refund of any moneys paid by a person under the provisions of chapters 18 and 19 of this title, or whenever a court of competent jurisdiction orders a refund of any moneys paid, the general treasurer shall, upon certification by the tax administrator and with the approval of the director of administration, pay the refund from any moneys in the treasury not appropriated without any further act or resolution making appropriation for the refund. No refund is allowed unless a claim is filed with the tax administrator within three (3) years from the fifteenth (15th) day after the close of the month for which the overpayment was made, or, with respect to determinations made under § 44-19-11 — § 44-19-14, within six (6) months from the date of overpayment, whichever period expires later.