Tower Controller described an emergency event when vehicles were cleared onto the runway by Ground Control but not coordinated via a recorded land line as required.

Narrative

Runway XXL was in use with the Visual Approach being advertised. Weather was VFR and visibility was unrestricted. I was providing training on the Local Control position and a CPC was working Ground Control (GC) at the GC position while also working XX. XX/GC informed us that there was an emergency BE35; arrival inbound. The Crash Phone was activated with an Alert 1 due to the BE35 leaking fuel out of his right wing fuel cap. The lead up to the BE35 landing was without incident. As the BE35 was landing; I answered a phone call regarding the emergency landing because XX/GC was busy coordinating with the emergency CFR vehicles. When I was on the phone; I heard XX/GC give CFR vehicles clearance to follow the BE35 down the runway. It is standard procedure for the CFR vehicles to follow an emergency aircraft; but it is verbally coordinated and recorded via the recorded line. When I saw the CFR vehicles enter onto the runway I acknowledged what they were doing and quickly approved the CFR vehicles to follow the BE35; but not via the recorded line. Safety was never compromised. Recommendation: have emergency vehicles change to the Tower frequency when they are requesting to proceed onto an active runway. Also; if I did not have to answer the commercial phone regarding the emergency; my situational awareness would have been better and I might have been able to see the runway incursion developing.