I'm filing a part-year resident of Colorado. It looks like they tax my year's taxable income from the federal taxes, not just what I made in Colorado?

For a Part-Year resident, the full-year form DR104 is used and your full income is listed on line 6...

BUT....the tax on line 7 should be based on only your CO income from line 36 of the form DR104PN.

In TurboTax, the full year's tax may be listed...UNTIL..you go thru the entire CO part-year interview and allocate what sub-portion of the full-year Federal income is CO income.   Print out your CO forms and check what you entered for those amounts on the DR104PN.  Especially, check out the decimal fraction multiplier on line 34 to see if that fraction approximates the proportion of your annual income was CO income.  Hen go thru the CO interview again to re-allocate if that fraction doesn't make sense.