The person who files there tax returns is the person who is appointed the administrator of the estate. That will go according to your state law. If they have a small estate and there is no argument among the different relatives over who should do it, there may be a very simple form to file with your state court. However, the procedures do need to be followed.
Once you have been legally appointed their representative, you can file their 2016 tax return. You will need to print the return, write "deceased" and the date across the top of the form and sign your name on the signature page with a notation "personal representative".
If they had a taxable income in 2017, someone will also need to file the 2017 return for them.
