First and most importantly, you must be the person recognized under law to be the personal representative of the person who died. (The executor of their estate.) If they have a Will, the Will will specify who takes that role. If there is no Will, and if you are not married, that role may automatically fall to another next of kin, such as a parent, sibling, or adult child. Before you can do anything else, you need to find out how the laws of your state handle the affairs of people who die without a will (intestate). If you aren't the official representative of the deceased, you might be able to apply to the court to be named as the representative. If there are other family members, and if they don't agree with your claim, the court will handle that dispute and assign someone.
Whoever the personal representative is (whether designated by the laws of your state or by a court)-- that is the person who files the final tax return.
Then, even if you are the representative, you might only have the job of tidying their affairs, and not actually be entitled to the money. If you aren't married and there is no will, the laws of the state might specify that their money goes to their children only, and not to you. Lastly, before any money can be paid to the heirs, all legal debts of the person must be settled; if they owe more money than they have in the bank, any tax refund would go to pay off debts instead of going to you or the other heirs.
I suggest you consult an attorney in your state to clarify what your rights and responsibilities are, especially if there is no written will.
