To clarify my response...The refrigerator can be on the small appliance circuit. The refrigerator is on a designated receptacle, that is not required to be on a dedicated circuit.
It is a good idea to put it on a separate circuit, if you don't like to drink your ice cream
I'll weigh in now. Fridge can be on small appliance circuit, dedicated 20 amp circuit, or dedicated 15 amp circuit. Most Sub Z's seem to require that they are on a dedicated circuit in which case the NEC would require this.