I got a K-1 for Colorado with:
Federal income modified for Colorado: -$10k
Nonresidents: Colorado source income: $240
Note that my investment is in an entity that further invests in various businesses across US. Which means I got 1 Federal K-1 for all the investments. And various state K-1s as part of the package. The total federal income is thus negative but Colorado source is listed as positive as shown above.
I am a non-resident for Colorado and no other income there.
I filed my K-1 in TurboTax Federal and it has not prompted me to file any state returns.
Do I need to file a Colorado state return?
per Colorado
You must file a Colorado income tax return if during the year you were:
A nonresident of Colorado with Colorado source income,
don't know exactly where you are in the step-by-step process but you should have or will come across a question "did you make money in any other state?" this should be answered yes