No one was injured in the incident, which occurred at 11:40 p.m., the LaGrange Police Department said, according to the report.
Police have launched an investigation and are seeking information from the public about the incident.
The incident marks at least the second time in July that bullets have been fired at a hospital. A man in Florida was charged earlier this month after allegedly firing into the fourth-floor window of Broward Health Coral Springs (Fla.) hospital from his car.