ASRS 2084286

I was working GC and coordinated to cross runway XX at [taxiway] 1. LC (training in progress) approved the runway crossing. I instructed Maintenance to cross RWY XX at 1 and turn right on TWY 2 for their engine runs. While I was reading a clearance I heard Local Control clear an aircraft for takeoff but I wasn't sure which runway. I then stopped reading my clearance and started scanning. I then told LC that I was still crossing runway XX and the trainer tried to cancel the takeoff clearance, but they said to "cancel their landing clearance." Then the OJTI keyed up and told Company to cancel their takeoff clearance, but I think they used the incorrect call sign. There was also a Company aircraft on final. Then the OJTI issued the cancel takeoff clearance with the correct call sign, and the aircraft turned off the runway. I'm not sure what recommendations to make other that we must all remain vigilant and continue to scan, use team work, and coordinate runway crossings accurately to prevent runway incursions.