I recall getting suspended in 9th grade for getting minor blue highlights in my hair, my first like 5 period teachers either liked it or thought it was funny, but then I got into a class with some old 70 something year old woman who stopped me on my way to my desk, dragged me to the friggin principal WHILE HE WAS GIVING A SPEECH in the cafeteria to report this grave injustice I had apparently committed against the school, they send me home on the spot and tell me to dye it out.
Now obviously I was too much of a little prick to listen to them ;P. So I came back the next day the same way, got through the entire day with, again, zero opposition, and then on my way to my last class, this same fucking teacher finds me again, and again, drags me out of class to the office, they suspend me for a fuckin week on the spot.
I was an A-B student before that -.-..lost alot of my drive from then on.
The point is, there arent generally any rules about that stuff, but particular people with be assholes about it, what was even more annoying was that other than that, I had short well kept hair, clean casual clothing, bright colors, absolutely nothing that would make me look intimidating. Plus there was another dude in the school, senior I think, huge guy, wore all black, skulls, peircings, all the works, and he had a spiked mohawk with each individual tip dyed a different color, Pink, purple, green, so on. Apparently this guy never got any trouble from it xD.
You did mention a private school though, Im not sure what the rules are in that case, they may actually be able to complain about that kind of stuff, but in public schools their shit out of luck unless they can make a big enough stink.
Regardless of the matter, theres alot more important things in schools that these people arent bothering to enforce, so going after people who didnt do a damn thing other than dress or groom a certain way is just their cheap way of pretending their doing any real good.