A: An excellent question! Let's see what information I have tucked up my wing.
1. Let's take a look at which raptors can be found munching on songbirds in Colorado: the Merlin falcon, the Prairie Falcon, the Peregrine Falcon, the Sharp-Shinned Hawk, the Cooper's Hawk, and the Northern Goshawk. We can eliminate the Northern Goshawk (the need much more privacy than a city allows). While it's unlikely that a Peregrine Falcon or Prairie Falcon would pop up in an urban/suburban back yard, it's possible, so we'll include it in this discussion.
2. The factor that first comes to mind is seasonality: While the Cooper's and Sharp-Shinned Hawks, and the Prairie and Peregrine Falcons all live here year round, Merlins are only found in Colorado in the winter. So, if you saw a bird yesterday that you think may be a Merlin, odds are it's something else.
3. The next thing to determine is whether it's a hawk or a falcon. All of our falcons (including the American Kestrel) have similar characteristics, the most obvious being the "chin straps" or "mustache marks" below their eyes. Below is a picture of these marking on each of the falcon species. If the bird you are seeing is sporting a mustache, it's a falcon; if there's no mustache, it's probably one of the hawks.
Another ways to determine if the bird is a Sharpie/Cooper's or a falcon is that Sharpies and Cooper's will be showing a lot of naked skinny toothpick leg when they're standing around.
Falcons, on the other hand, sit a little closer to their feet, and their legs are stockier and more feathered:
In that montage, you can also see that falcons tend to have dark eyes, whereas the little hawks have orange, yellow, red, or pale eyes.
4. It was hard to find or create a side-by-side comparison of the birds, so instead I drew a picture to help you see the difference in coloration and size. I compared the size of the birds to a one-liter water bottle:
5. And, finally, there's habitat preference. In a city like Denver, even on the outskirts, you are far more likely to have Cooper's Hawks and Sharp-Shinned Hawks dining on your backyard songbirds than any of the falcons. In the winter, a Merlin would be more than happy to help you thin the sparrow population a bit, but if you do see one you're very lucky because they're aren't exactly plentiful or common in these parts. I'm not saying that it's impossible to see a falcon in your backyard, but it's definitely less likely than the other options.
I sure hope that helps! Please comment below or email me at firstname.lastname@example.org with further questions, clarifications, or even pictures to ID! Thanks for reading!