Yes. You would file as a non-resident OK Form 511 NR.
On your OK Form 511 NR, you are allowed to deduct either your OK standard deduction or your Federal Itemized deductions.
When you entered your Oklahoma gambling winnings and all gambling losses in the federal sections of TurboTax, the gambling losses will transfer over to the Oklahoma return as part of your itemized deductions. There is no additional place to enter these losses in the OK return. There is no distinction for state of gambling loss.
You could still wind up owing some tax to Oklahoma even though you claim losses up to the extent of your gambling winnings. That's because OK computes a nonresident taxes based on their federal Adjusted Gross Income, then applies a percentage to the total tax based on the ratio of your income from OK to your total income.
Please feel free to post any additional details or questions in the comment section.
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