@PhoebeRobertswill know about OK particularly, but except for CA most state K-1 stuff does not export.

I agree, state info almost always has to be input manually.

For an OK resident, you adjust income on Screen 51.041, not in the K-1 input screen. 

Withholding you can enter in the K-1 input screen under Credits and Withholding.

For a non-resident, you can probably use the State Source column in the K-1 input screen, but all my people are resident, so it's been a long time since I had that situation.

do you work with Oklahoma Partnership Composite Return.  Any idea why the Oklahoma withholding for each nonresident partner is automatically flowing to Form 514 Part 1 Line 7 from Form 500-B?

I don't do any Oklahoma composite (because my people are mostly resident), but I'll look at it in the morning. 

You just need to indicate that you didn't withhold anything from the partners, if that's the case.