Since you and you and your spouse are dual military, filing jointly with Georgia as your permanent residence while filing as non-residents in Colorado., you may still owe Georgia state taxes because Georgia residents are taxed on all income, except tax-exempt income, regardless of the source or where derived., including military pay and any other out-of-state earnings.
If military pay is your only income, it is likely exempt from Colorado taxes, but Georgia still taxes it. For more details, you can visit the Georgia Department of Revenue (click on full-year resident) and the Colorado Department of Revenue.