Try doing a Google search for your state's name, plus "mandated reporter law" ... such as "georgia mandated reporter law".
Check out this resource for info about
mandated reporter laws.
That should help you find the law, which will probably also list the penalty for false reporting. In some states the only remedy is to sue the person making false reports. You would have to have PROOF that the person was maliciously making reports. The problem is that the person would probably give a defense of having made the report "in good faith" believing it to be true. Your word against theirs. So the cases are rarely brought to court as they can't be proven enough to convince a jury or judge.
In some states you can report a false report to the police as they've made it a criminal rather than a civil offense. Maybe having a police officer show up at their door would be enough to silence them.
If you're sure it is your ex, you could try getting an attorney to send him a letter stating that continued false reports will result in a lawsuit. People do not like getting letters from attorneys, so that might help stop the problem.
Here's information on laws regarding
central registries in each state.
Also- you might want to read the page in my signature line here about divorce, separation and CPS... and ask your ex to read it too.