I think it depends on the State or the county as to who is responsible for reporting an abuse. For example I live in Florida and our county policy is a mandatory reporting of child abuse or neglect by the teacher or other staff member who knows or has a reasonable cause to suspect. We would call the State's Department of Children and Families hotline.
If you suspect abuse, you can call your state's hotline. You might be able to report a case anonymously, although I think it is better if you give your name. That way if they have questions, you can answer them honestly. We need to protect the child first.
When a child reports abuse to a teacher, by law the teacher must ask the child exactly what happened and take notes of everything (it is easy to forget the smallest detail that may prove to be extremely important in the future), ask the name or relationship of the adult that hurt them, when the incident occurred (i.e. Friday night or Saturday morning?) did the perpetrator use their hands, feet, or a foreign object to assault the child, etc. The teacher should: ask someone to temporarily take over the duties of their classroom, the child reported to a person he/she considered trustworthy, that should not be broken. Once the teacher has as much information as he/she believe they can reasonably obtain from the child. Then report the incident to Child Protective Services. If it is a government holiday and they happen to have the day, or week off, call the police with the report. Regardless of which agency you contact, make a copy of the notes you took for yourself... School personnel, Clergy, Child Care workers, and persons in law enforcement, healthcare providers, just to list a FEW are mandated reporters; meaning: they are MANDATED BY FEDERAL LAW TO REPORT ANY AND ALL INCIDENT OF CHILD ABUSE. THEY MUST REPORT FIRST HAND (THEMSELVES) WHENEVER A CHILD REPORTS ABUSE TO THEM. THEY ALSO MUST REPORT ANY INCIDENT THAT APPEARS A CHILD MAY BE ABUSED, OR THAT A CHILD COULD BE IN AN OMINOUS SITUATION. If you suspect abuse, follow up. Sometimes teachers make horrible choices too, and decide to tell the parents. Unfortunately, this is the worse thing they could possibly do. It is the cause of many child fatalities. Caseworkers also refuse to follow up, they are federally funded, ask for supervisors and continue demanding action until it is taken and the child is safe. Persons in this role need to realize that it is their duty to put the child first, they are not supposed to worry about the abusive parent(s) being a friend to them.