Yes. The income from the rental property is taxable to New York (NY). If you have a profit then you will have NY tax liability. Prepare the NY return first as nonresident, then prepare the Colorado (CO) return.
CO will give you credit for taxes paid to another state on the same income. The credit for taxes paid to another state on the same income is used on your resident state because they do not want you to pay taxes twice on the same income. As the resident state all worldwide income must be included.
The credit for tax paid to another state on the same income will be the lesser of:
- the tax liability actually charged by the nonresident state, OR
- the tax liability that would have been charged by your resident state