Is it legal?

What is the name of your state?New York
I run an in home child care center and recently a 7 month old had fallen in my kitchen and had received bruises. The mother took the daughter to the hospital for testing, which I was never informed of until recently. The mother had informed me in writing that the hospital had written information with my name on it claiming I was negligent. Is this legal, considering I had no knowledge of the accusations being said and I was never given a chance to explain what happened to the doctors.

what mom did was perfectly legal. the child was hurt while in your care. if the licensing agency starts an investigation, then you can explain what happened.