No, you will not need to indicate you lived in another state. However, you will indicate you earned income in another state (CO). You will make that selection in the "Personal Info" section, "Other State Income" near the bottom of the page.
Your responses there will trigger TurboTax to generate a non-resident CO state form. You will enter the W2 information in the federal interview. You will be entering any state taxes that CO withheld on your Form W2 there.
Once you complete the federal interview anything applicable to CO will transfer to that state interview.
In the CO interview you will arrive at a page entitled "Colorado portion of wages". Assuming all the wages for the year (W2 box 1) show as CO wages (W2 Box 16), you will need to prorate based on the number of days worked in CO.
Once you complete the state interview if you have paid more than required to CO for the 2.5 months there through withholding, you will get a refund.
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