U.S. Supreme Court
Pierce v. Society of Sisters, 268 U.S. 510 (1925)
http://supreme.justia.com/us/268/510/case.html
“The fundamental theory of liberty upon which all governments of this Union rest excludes any general power of the State to standardize its children by forcing them to accept instruction from public teachers only. P. 535.”
Yes. Private certified teachers are allowed, also. California law recognizes this.
Disclaimer: IANAL and this ain't legal advice.