Estate Tax applies to the Minnesota assets of a decedent's estate. 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.In most cases, the personal representative will have to file a final lifetime individual income tax return, usually using federal tax form 1040. What are the tax consequences of residency status under the individual income and estate taxes? The personal representative of a probate estate in Minnesota is required to file any necessary income tax returns for the deceased.