The answer to your question is yes. If you have a Form 1099-R for the Oklahoma Teachers Retirement System, then you should check the box (or fill in the radio button) next to the "Oklahoma Government" entry.
The Oklahoma public schools system is an extension of the local government, and so this makes such a pension technically a "government" pension from Oklahoma. Specifically, under Oklahoma tax law, taking this election will allow you to exclude up to $10,000 of your pension income from Oklahoma state income taxation (although it remains fully-taxable by the IRS under federal law).
Please see the screen-capture image attached to this answer for an example of how to make the correct data entry on the federal 1099-R pension interview; simply click the image to open.
Thank you for asking this important question.
