Wow! Great question!
Getting a little close to the "Evil Empire" otherwise known as Denver! LOL
I checked both the Arapahoe County Sheriffs site, CBI's site, and my own counties site, and no where does it ask whether or not you are a US citizen. They only ask if you are a legal resident of Colorado and legal resident of the county in which the permit is being applied for.
Quick disclaimer: IANAL!!!!!!!!!!!
I believe that you would have to adhere to Federal Law on this. If you're legal to purchase and own a firearm, then you should be able to apply for a permit in Arapahoe Co, CO. If you're status is "Resident Alien", and you have a clean record, you should have no problem. Anyone out there know if there are more alien status' that are valid in the US for firearm ownership?
The only parts of the app that says anything about being a US citizen is the part where it asks if you've ever denounced your US Citizenship, and if your an alien ILLEGALLY in the US (dumb question IMHO).
Quick qualifier question: Have you ever bought a firearm in the US thru legal channels
? (Form 4473 filled out and submitted, thru the NICS check, etc). If yes then you should be good to go.
Link to the criteria for Arapahoe County CCW: