There is not a lot you can do except to get a lawyer involved now or wait and see what action CPS wants to take regarding the complaint. I am not overly optimistic about dealing with CPS and getting things closed quickly. That being said, don't count on CPS doing the "right thing".
I am not intending this to be legal advice, because I don't know the particulars of your situation. Call me if you would like to discuss this or other isues.
When ever CPS starts an investigation that may target you, you need to get a lawyer.
Answers on Avvo are for general information purposes only and should not be relied upon as legal advice. No attorney / client relationship is created by providing this answer. For specific advice about your situation, you should consult a competent attorney of your choosing.
The police and CPS can question your child with or without your permission, and without even notifying you afterward. The school did not hold a CPS investigation - they reported a concern to CPS who opened the investigation.
You should hire a lawyer who has experience with CPS. Many times it requires nothing more than cooperation, but that is NOT always the best thing to do. Many times it can be settled with a house visit and some times with some "parenting" classes, and nothing more comes of it. But, it really depends on what your child said.
Do NOT berate your child about what was said; instead get a lawyer involved. Your child will not understand what s/he should say, and the effect of anything they do say - true or not true.