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playbingo17,

 

Opus17 is correct.  The Colorado income tax booklet instructions DR104 states:

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Each year you must evaluate if you should file a Colorado income tax return. Generally, you must file this return if you are required to file a federal income tax return with the IRS for this year or will have a Colorado income tax liability for this year and you are:
A full-year resident of Colorado, or
A part-year Colorado resident who received taxable income while residing here (you must file the DR 0104 along with the DR 0104PN), or
Not a resident of Colorado, but received income from sources within Colorado (you must file the DR 0104 along with the DR 0104PN). 

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Assuming you are in TurboTax because you need to file a return with the IRS, the first requirement is fulfilled.  The non-resident requirement is also fulfilled because Colorado income tax is based on a fixed 4.4% percentage of your federal taxable income.  So, yes you will need to file in CO as well as NM.

 

The amount of tax you will be paying to CO will be 4.4% of the $600 winnings, $26.