I am very sorry for your loss. You do have the option of filing jointly if your spouse passed in 2019. The Married Filing Jointly status will offer you the most advantageous tax rates, along with the highest standard deduction.
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You may file jointly. There is a box to check in your spouse's information that they passed away and a place to indicate the date. You may not be able to e-file, either due to a bug in Turbotax (this is unclear) or because the IRS routinely blocks the SSNs of deceased taxpayers to reduce fraud. If you can't e-file, print your return, sign in your space and your spouses space with "personal representative" and mail the return.
You should file jointly for 2019 for the best tax advantage. When entering your spouse's information in the My Info section one of the screens will have a checkbox for "This tax filer passed away in 2019". Make sure you select that checkbox.
Now depending on serveral factors, you may not be able to e-file the tax return. If the entity handling the final arrangements (usually the funeral home) did their job, they notified the Social Security Administration of their passing. The IRS pulls taxpayer information from the Social Security Administration around Dec/Jan every year. That's how the IRS gets notified of someone's passing.
When the IRS is aware of someone's passing, they lock the social security number so that it can't be used fraudulently. While there are numerous errors this can generate when you attempt to e-file a tax return with that SSN on it, the most common error is "SSN LOCKED".
So if you get that error when attempting to e-file, you have no choice but to print, sign and mail the return to the IRS. There is absolutely no work around either, by intent and design.
If you have qualifying dependent children, you may also qualify to file your 2020 tax return with a filing status of "windowed", which will give you a higher standard deduction.