You could start by asking to see the school's budget or ask if they have any income from Federally funded grants/etc - they might or might not share the information with you, depending on the school. It may be different in other parts of the US, but based on my experience having been involved with several different private schools in my small part of the world - I'd be very surprised if a private school was receiving any DOE funding, unless it was coming through a program that benefited students from low-income families.
Students with special educational needs that would be serviced by IDEA in public school are eligible for IDEA services as private school students, but the services are usually provided *through* the public schools: the student is evaluated through public school, then if the student qualifies receives the services through the public school. Some services can only be offered *at* the public school, so the student can't participate in them if they remain in private school; some services can be received outside of the public school day or offsite. The funds from DOE that support those services are managed by the public school district, not paid directly to private schools (at least that's how it works in my state).
Although IDEA is not something that our (local) private schools administer directly, ADA protection is something every private school I've been involved with takes very seriously. It's actually been much easier for my 2e children to receive appropriate accommodations through private school where it wasn't necessary to draw up a 504 plan than it was in public school.
Not sure any of that helps! Do you think your child's school receives Federal funds directly or through a grant?
Best wishes,
polarbear
