B737-300
Flight Crew Air Transport Pilot (ATP)
Workload; Communication Breakdown; Distraction
Deviation / Discrepancy - Procedural Published Material / Policy; Ground Event / Encounter Vehicle
Flight Crew Took Evasive Action
Procedure; Human Factors; Environment - Non Weather Related
Event began during pushback. Ground crew told me that Operations needed to talk to me about a prosthetic limb that had been left behind. We had briefed a single engine taxi and; after the first engine start; I asked the pushback crew to stay while I talked to Operations. Operations relayed that they had a prosthetic leg that had been left by a customer and needed to know if we wanted to return to the gate for it or send it on the next flight to the customer's destination. They asked us for the customer's name and destination. I asked the flight attendants if they could identify the customer and get the requested information. The pilot not flying was getting a new release time from Ground Control and was not directly involved in the Operations/ground crew/cabin crew conversations. The Flight Attendant; who identified the passenger; relayed to us that the limb was for exercise and not required immediately by the passenger; but had to go back to get the name and destination information. We decided not to go back to the gate and the pilot not flying called Ground to tell them we would be ready for taxi in a minute. I cleared the tug crew off but; when they replied; I did not watch them leave. I went immediately back to the service interphone for the customer information. Bringing back my attention to the flight deck; the pilot not flying completed his flows and set the flaps. We completed the flight control check and the pre-taxi checks. Since Ground had cleared us for taxi on the 'ready in a minute' call; I released the parking break and bumped the throttle up. As I sat up in the seat to clear; I saw the corner of the tug (it was not visible until I sat up) and immediately braked to a stop. I think the aircraft had moved less than a foot. After the time that had seemed to pass; it did not occur to me that the tug would still be there; even though I had not followed the normal procedure for clearing the ground crew off. The ground crew didn't do anything non-standard. I could have avoided the situation by: First; clearing the ground crew off normally; despite the fact that they had provided the initial message; they were not required. Secondly; not initiating the post-start flow until the tug was visually cleared with the required pin and wireless kit; etc. or; deliberately clearing the full path of the aircraft before releasing the parking brake.
While this was taking place; I (Check Pilot in right seat) was heads down receiving a new wheels-up time since I noticed that our last wheels up time was going to expire. While I was doing this and being heads down; I heard the Captain clear the ground crew off. I was still occupied by waiting to get our new wheels-up time. After getting the new time; I looked out of the aircraft and did not see a pushback crew or a tug used to push us back. Also; I saw the Captain communicating with someone else on the radio or interphone; after seeing this and not noticing any Ground Crew; I thought he had seen them depart from the aircraft. After he came back from his radio or interphone communication; I started my flows to prepare the aircraft for taxi. After performing these items; we conducted the Before Taxi Checklist and I contacted Ground Control for our taxi instructions. The Captain and I confirmed clear right and clear left before starting our taxi. The Captain released the brakes and pushed the one throttle forward since we were conducting a single engine taxi. In the future when I am conducting a [review]; I will instruct the other pilot to never remove the brake until we both have confirmed that all personnel are clear of the aircraft and all items are complete; i.e. coordinating how to get a passenger's belongings back to them.
A B737 flight crew began pushback while tug was still under the aircraft's nose.  Proper disconnect procedures were not followed through due to flight crew distraction of dealing with Operations.