Hello I am a licensed attorney here to help you with your question, please review my response and do not hesitate to ask for clarification.
The administrator in most situations would be the spouse, but if the spouse was not appointed the Administrator would file a tax return for the Estate,
A personal representative of an estate is an executor (executrix), administrator (administratrix) or anyone who is in charge of the decedent's property. The personal representative is responsible for filing any income tax return(s) and the estate tax return when due. Please refer to Publication 559, Survivors, Executors, and Administrators, for additional information on personal representative responsibilities.
The IRS allows a surviving spouse to file joint returns for the taxable year in which the death occurred and, if the death occurred before the date that the decedent's return for the immediately preceding year was due, for the taxable year immediately before the year of death.
The Administrator should discuss the personal tax return issue with the spouse to make sure their is no problem with two people filing a personal return for the deceased.