You don't need to be a citizen, just have residence, ie a drivers licence.
I bought a gun when I stayed in Colorado in the 80s, and I'm a Swedish citizen.
Don't have to be a citizen, but have to be either a permanent resident (green card), have a hunting license valid in the residing state or be a foreign law enforcement rep of a friendly gov plus some unclear rules on visa waiver (maybe OK if you are from EU, Japan or Australia). Sweden qualifies with the waiver.
https://www.quora.com/Can-a-visitor-to-the-USA-purchase-a-gun-and-own-it-legallyMight be different now, but all you needed in Co when i was there was a drivers license.
And all you needed to get a drivers license was an address, get fingerprinted and passing the test.