How old can a person legally move out of a parents house in Colorado?

This appears to be the definition in the Colorado law that you want.

It comes from TITLE 19 CHILDREN'S CODE

ARTICLE 1 General Provisions:

"[definition] (45) "Emancipated juvenile", as used in section 19-2-511, means a juvenile over fifteen years of age and under eighteen years of age who has, with the real or apparent assent of the juvenile's parents, demonstrated independence from the juvenile's parents in matters of care, custody, and earnings. The term may include, but shall not be limited to, any such juvenile who has the sole responsibility for the juvenile's own support, who is married, or who is in the military."