We send a single engine to auto accidents. Unless there's reported entrapment, then the 3 closest Apparatus (it could end up 3 engines, 2 engines and a Quint/Ladder, 2 Quints/Ladders and an engine, it just depends on location).
But we dont even dispatch an engine to every single accident. I'm not sure what the dispatch protocols are, but often just a single EMS unit with PD will respond (I remember during our ridealongs in the NREMT part of Academy, we had an auto accident two blocks away from a downtown fire station (engine and ladder) and we back boarded two patients and loaded them both up and transported without ever calling for Fire). I think it depends on how the call is initially routed, if it goes to PD first they'll just call for the ambo. I think if the call gets routed to EMS first they'll call us... sometimes. Right now all three services dispatches are completely separate. Theres plans in the works for a new, state-of-the-art dispatch center that'll have all 3, so maybe that'll affect response matrices when that goes into effect...