Only with a tiny bit of information, and only for mandated reporters, I believe.
In NY, certain people are "mandated reporters" of suspected abuse and neglect, which means by definition the report can't be anonymous. Schools are mandated reporters. They would call the mandated reporter 800 number and give the reason they believe the child may be abused or neglected. Then they follow up the report with a written report. They can ask for the findings of the report, but the findings are generally only one word, "indicated" or "unfounded."
Calls from the general public go to a different number, and callers do not have to give their name or follow up in writing. I do not think they are entitled to know if an investigation is "indicated" or "unfounded,"
All callers while discussing the situation with the NYS hotline are told if the hotline is planning to do an investigation or not based on the information given. The criteria by no means are that the caller can prove anything; investigation might not be done if the caller did not report something that seemed to mean the child could be in danger (immediate or future). But is no investigation is planned the caller is entitled to a reason and can certainly request a supervisor if the reason does not seem like a good one.
The callers identity is not shared with the family investigated and the details learned are not shared with the caller. This is intuitive. For example, the bruise example above, a school could have called it in, a parent could have given the investigators permission to speak to the pediatrician, who might confirm the follow up visit after ER, etc. and that nothing neglectful came to mind, and the child does have a greater than average number of injuries because of ADHD and partial deafness in one ear, causing balance issues that mix hazardously with poor impulse control.
The parent could share all, part or none of this medical info with the school, it's up to the parent. So when CPS finds all this, they only say, "unfounded," to the school. The medical information stays with CPS unless the parent gave it to the school.
This also prevents any person or agency to use CPS as a private eye.