If you are using TurboTax Online, you will have to create a separate account.
If the deceased person meets the filing requirements, a tax return will need to be filed. The surviving spouse can file if there's no executor of his estate. If they weren't married, a survivor of the deceased can file.
You will use the taxpayer's SSN, not yours when you file taxes for a deceased taxpayer. For more information, refer to the Turbotax article regarding filing a final tax return and the IRS article File the Final Income Tax Returns of a Deceased Person.