File the final income tax returns of a deceased person for current and prior years, pay any balance due and claim the refund. File an estate income tax return.File Form 706 for the estates of decedents who were either. U.S. citizens or U.S. residents at the time of death. What is the estate tax? How do I file the estate tax return? For paper returns, the filer should write the word deceased, the deceased person's name and the date of death across the top. You'll need the person's Social Security number and certified copies of their death certificate for most agencies and programs. Social Security and Medicare. Form 1310 is a tax form that is used to claim a refund for a deceased taxpayer.