Yeah double check your local and state laws.
But anecdotally, everywhere I worked if we happened across an accident scene, we'd stop and call in the "Still Alarm" to dispatch and investigate for any injuries. This was the same whether I was working for a private IFT only company, an FD 911 only ambulance or a private company with combined 911/IFT services, regardless if we were in our 911 response area or not. If it was in my 911 service area and we did not have a patient on board, we would officially be assigned the call. If it was outside our jurisdiction and/or back in my IFT only days, our dispatch would notify the appropriate agencies dispatch and we would stay on scene to treat any injuries until the jurisdictional provider showed up and took over. If we were enroute to another call, dispatch would simply assign another unit to the original call, and treat it the same way if the "still alarm" came in as a normal dispatch and they reshuffled units to go to the closer calls (i.e. "Unit X, change in response to a closer call, TC at ABC Intersection.....BEEP BEEP BEEP Unit Y, respond to the fall at DEF Care Facility....")
Now things got a little trickier if we had a patient on board, but fortunately the rules have tended to stay the same for me across the different services I've worked for. What matters is how stable is my existing patient in the back? For a stable patient (most all BLS and code 2 ALS transports) the same thing, we'd stop, call in the still alarm and another unit would be dispatched, while we provided initial triage, care and treatment until they took over and we could continue transport.
For an unstable patient, things get trickier, but the rule of thumb was basically pull up to the scene, and simply inform someone there on the scene "Hey, we see the accident, I've called it in to our dispatch so another unit is responding, but unfortunately we can't stop because we've already got a critical patient on board that needs to get to the hospital now". That way you (hopefully) avoid the problems of "OMG That ambulance just drove by the accident with out stopping!"
Fortunately in my 3+ years I've yet to actually need to do any of this.