Whether the school has liability for the injury depends upon all of the facts and circumstances of the injury. It may be liable, but you should consult a personal injury attorney to get advice concerning your rights under the circumstances.
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A consultation with a local attorney will allow analysis of the specific issues necessary to determine whether you have a sound claim. Was your child's use of the gym at that time permissive? Supervised? Did the injury involve use or misuse of any equipment? These and all of the other facts and circumstances of the incident must be specifically considered in order to make a good assessment of your potential case. Look for an attorney who will evaluate your case at no or very low cost.
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For the school to be liable, they must breach some duty of care. Whether that occurred would require a review of the facts. Certainly breaches of care may occur in many respects, such as a failure to properly supervise, a failure to maintain playground equipment, or, perhaps, even a more active role of a school employee that caused or exacerbated the injury.
You should consult with legal counsel.
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