Colorado does not appear to have a statutorily defined procedure for emancipation. It recognizes emancipation in its statutes:
Quote Quoting Colorado Code 19-1-103. Definitions
(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.
and it is my understanding that a court will recognize a minor as emancipated. Without a statute, it's difficult to suggest the procedures; you may wish to inquire with your local court to see if there are standard forms for petitioning for emancipation. But the statute suggests that you can't emancipate over the objection of your parents.