Yes, depending on the state.  Licensed child care or pre k centers may or may not be in a position to handle stool, change diapers or dispose of them under certain OSHA government laws.  For example, my pediatric office refuse collector refuses to take diapers and therefore we provide bags for parents to take soiled diapers home.  It also depends if the staff has been protected with hepatitis B vaccine and if they have the required cleaners and surfaces for changing.  Most schools feel if your child is over three, they should be trained. Many typical child hood viruses are shed in stool and urine for sometimes weeks after the illness; therefore for the health and safety of the class and teachers, most will call the parent to get their child. Certainly with illness sometimes accidents happen, but check your school policy and speak with the director.
 
Wayne Yankus, MD, FAAP
expert panelist: pediatrics