I'm taking the class now, (Final written tonight and driving session on Saturday)and was told that you have to have a valid license for the apparatus you will be driving on the course. A regular license from NY should work if you will be driving an ambulance or brush truck. You will probably need a CDL or class B if you will be driving an engine or squad. Also note that you will need a written letter from the chief if you will be using another company's vehicle.
You might check MFRI's web site to get a phone number to verify this. The URL is:
http://www.mfri.org/