No. If you moved from Oklahoma to Oregon in 2015, you will file part-year returns for each state. Oklahoma will only tax OK income and Oregon will only tax OR income. You will reply 'no' to that question.
That question would come into play in a situation where you are an Oregon resident, but worked in Oklahoma for a short period of time. Non-resident taxes would be paid to Oklahoma, but you would still be required to claim the income on your Oregon Resident return. Oregon would offer a credit for the taxes already paid to Oklahoma.