Can a 17 year old dropout of high school without parental permission

No - at age 17 you are not an adult, and must still comply with your parents rules.  You will not be able to drop out of school unless they consent, and if you do not attend you will be truant.  Besides the legal answer, as a mom I would say you have to stay in high school and get your diploma, you will regret it if you do not.  If you are unhappy with the school you are in. talk to the guidance counselor about vocational or trade school, or some other laternative to get your highschool diploma.