If you want a refund of the January 2016 W-2 income taxes withheld (in error) for Colorado, then you will want to file a Colorado nonresident state return and make a claim for a refund. As it sounds like you were Texas residents all year in 2016 (living in an apartment or a house doesn't make a difference here with respect to state residency), neither of you have Colorado-source income for 2016.
Thus, you have one of two choices as to how to handle this.
One, you can file a Colorado nonresident state return, report no state of Colorado income on it, but input the amount of the state taxes withheld by the employer. If you file such a return, you should get a refund of all the Colorado state tax withholding shown in W-2 Box 17.
Two, you can chose not to file a Colorado nonresident return (i.e, you really don't have to if you don't want to), and the Colorado state treasury will receive it as unclaimed property, after the 3-year statute of limitations on requesting tax refunds runs its course.
Those are your Colorado options; and you are absolutely correct in that Texas has no personal income tax system, so there is nothing for you to file there.
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Thank you for asking this question.
