The Not Required to File section on page 7 of the instructions for Oklahoma form 511 has information on filing an Oklahoma return when not required to do so. It states:
Check the box if you do not have sufficient gross income to require you to file a Federal return. You had Oklahoma tax withheld, made estimated tax payments, or qualified for Oklahoma earned income credit or Tornado Tax credit.
Finish the top portion of the return by completing the "Exemptions" section (part G on the diagram on page 6).
Complete line 1. Enter the amount of your gross income subject to the Federal filing requirement. In most cases, this will be the same as your Federal Adjusted Gross Income. (Do not complete lines 2-19.)
Complete lines 20 through 39 that apply to you.
If you qualify for the Federal earned income credit, you qualify for Oklahoma earned income credit. Enter 5% of the Federal earned income credit on Form 511, line 29 (do not complete schedule 511-F).
Sign and mail the return. Include your W-2, 1099, or other statements to substantiate any Oklahoma withholding.
Note: If you do not have the sufficient gross income to require you to file a Federal return and you did not have Oklahoma tax withheld, make estimated tax payments or qualify for Oklahoma earned income credit or Tornado Tax credit, do not file an Oklahoma income tax return (Form 511).
This information applies to all years of the UltimateTax software.