Enclose a copy of your spouse's death certificate when you file the final Minnesota income tax return. In most cases, the personal representative will have to file a final lifetime individual income tax return, usually using federal tax form 1040.Minnesota imposes a tax on the estates of individuals who are residents of the state when they die or who own tangible property (typically real estate) in. The personal representative of a probate estate in Minnesota is required to file any necessary income tax returns for the deceased.