If upon the decease of a person leaving an estate liable to a tax under the provisions of chapter 22 of this title, a will disposing of the estate is not offered for probate or an application for administration is not made within three (3) months after the decease, the tax administrator may in his or her discretion, with the approval of the attorney general, agree with the persons interested in the estate as to the value of the estate and the amount of the tax to be assessed on the estate, or the tax administrator may apply to the probate court for the appointment of an administrator of the estate, and the probate court upon the application shall appoint an administrator of the estate.