As your brother's personal representative, you should complete a tax return for him. You must write the word "Deceased" across the top of the tax form, followed by the decedent's name and date of death. If you are using tax software, there is a section where you check a box that the taxpayer is deceased and enter the date of death. As you are not a surviving spouse, you must complete IRS Form 1310 to obtain any refund. Lastly, sign your name in the signature box followed by the words "personal representative."