If you are the spouse of a service member and you moved to Colorado only to be with them on military orders, the wages and tips you earn in Colorado are not subject to Colorado income tax. For state tax purposes you may choose the service member’s residence or domicile, your own residence or domicile, or the service member’s permanent duty station.
There is nothing to apply for. File as a nonresident and ask your employer to stop withholding Colorado income tax from your wages.
Your marriage certificate, the service member’s orders assigning them to Colorado, and proof of your state of legal residence.