Typically, yes, you would file in both states.
You would prepare the Colorado tax return first since that's the state you left and is your non-resident state. Then, prepare a New Mexico return. Since you lived in New Mexico when you received the income, you will prepare that one but will get a credit for taxes paid to Colorado.
For New Mexico, since you didn't earn income from New Mexico sources, you would file for a credit for the taxes paid (withheld) for Colorado.
When would I have to file returns in more than one state?