http://www.ed.gov/pubs/RegPrivSchl/index.html
of note are the teaching credentials (state mandated and state run) and the curriculum (determined by the state)
No significant deviation from state brainwashing is allowed. same teachers and same material.
I’m not sure which state you’re talking about, but I dug up this gem:
I don’t remember the local public schools doing any such thing. On a side note, it seems that archive was last updated nine years ago.
I doubt the education code is updated at more than a snail’s pace.