I was recently employed with a swimming pool management company in Colorado. I worked for a week and a half before deciding to seek another job for a variety of reasons. The employee handbook states that they request a 1 month notice, but goes on to state that I am "required" to give at least 1 week notice. Where does this "requirement" come from? As far as I know, I am employed at will. Is it just the employer's strong wording to keep people form quitting on a whim? Or is there really some Colorado law out there requiring one week's notice?
Thanks for any advice.

The requirement for a month's notice is likely toothless. They cannot refuse to pay you for the time worked and, given the amount of time you worked, you won't lose any vacation pay (which could happen for someone that worked longer).

Colorado doesn't have a stautue that requires anyone gives notice to their employer. Colorado follows the at-will doctrine.