From the forms instructions:

The filing status for Oklahoma purposes is the same as on the
federal income tax return, with one exception. This exception
applies to married taxpayers who file a joint federal return where
one spouse is a full-year Oklahoma resident (either civilian or
military), and the other is a full-year nonresident civilian (nonmilitary). In this case, the taxpayers must either:
1. File as Oklahoma married filing separate. The Oklahoma
resident, filing a joint federal return with a nonresident
civilian spouse, may file an Oklahoma return as married filing
separate. The resident will file on Form 511 using the married
filing separate rates and reporting only his/her income and
deductions. If the nonresident civilian also has an Oklahoma
filing requirement, he/she will file on Form 511NR, using
married filing separate rates and reporting his/her income and
deductions. Form 574 “Allocation of Income and Deductions”
must be filed with the return(s). You can obtain this form from our
website at www.tax.ok.gov.
-OR2. File as if both the resident and the nonresident civilian were
Oklahoma residents on Form 511. Use the “married filing joint”
filing status, and report all income. A tax credit (Form 511TX)
may be used to claim credit for taxes paid to another state, if
applicable. A statement should be attached to the return stating
the nonresident is filing as a resident for tax purposes only.
If an Oklahoma resident (either civilian or military) files a joint
federal return with a nonresident military spouse, they shall use
the same filing status as on the federal return. If they file a joint
federal return, they shall complete Form 511NR and include in
the Oklahoma amount column, all Oklahoma source income of
both the resident and the nonresident.