Usually in Illinois a home school enjoys the same status as that of all other private schools. We are not under the jurisdiction of the public school system at all and can direct our own schedule, philosophy and curriculum. Our independent identity is very important to maintain even when participating part-time in the activities of the public schools.
Home schooled students (like all private school students) are entitled to participation in any "for credit" class that is offered by the public school. This is true because of the state's interest in ensuring that all children have an access to an education. Extracurricular activities and also sports are treated quite differently. I am addressing sports in particular in this document.
Interscholastic high school sports are guided by the Illinois High SchoolAssociation (IHSA), which is an organization independent of the public schools with its own rules.
Any school, public or private may belong to the IHSA and form its own teams to play in its leagues. A home school is necessarily different from other private schools however, because it usually does not have enough students to form a team of its own. Therefore homeschoolers are often in the position of wishing to join a team representing another school, usually the neighborhood public school.
The public school in question may be amenable to homeschooler participation, but they are held by IHSA rules which specify that all members of the teams that represent it, actually attend that school. The reasons for this are easy to understand. A school should not be able to use "ringers" or superior athletes who do not even attend their school to attain an unfair advantage over other schools in their league.
So if a public school wishes to offer this opportunity to a homeschooler in the area, how can it be done? IHSA 2003-2004 rules state that a homeschooled student may participate if the student is "enrolled at the member high school, ...taking a minimum of 20 credit hours of work at the member school or in a program approved by the member school, and the student must be granted credit for the work taken either at the member school or in a program it approved." (quoted from "Illustrations for Section 30.10 of the By-Laws"; also see "Illustrations for Section 4.010 of the By-laws")
This analysis does not constitute the giving of legal advice.