Legal Question in Personal Injury in Ohio

Probably not unless the school employees did something reckless to cause the injury. Assuming it is a public school it is very unlikely you can bring a negligence action against the school. Ohio public schools have qualified immunity from such lawsuits which means they can't be sued unless their conduct is far more egregious than mere negligence. Plus, even if you could sue them, if you have health insurance to cover your childs bills the school does not have to pay those same bills paid by insurance. The school would only have to pay whatever "out of pocket' expenses you actually owe after insurance, write-offs etc... If it is a private school this answer would be very different.