Flight Crew Air Transport Pilot (ATP); Flight Crew Flight Instructor; Flight Crew Instrument; Flight Crew Multiengine
Flight Crew Last 90 Days 90; Flight Crew Total 9500; Flight Crew Type 400
Communication Breakdown; Situational Awareness
ATC Issue All Types; Conflict Ground Conflict; Critical
Flight Crew Took Evasive Action
Airport; Human Factors; Procedure
Ground control gave us a clearance to taxi via B; B2 and cross Runway XY at B2.  We headed south on B; turned right (west) onto B2 to cross runway XY.  As we were on B2 crossing runway XY; I heard ground controller state 'aircraft on B4 stop; hold position; aircraft on B4 stop immediately.'  We were on B2 but I had been listening to other calls on ground and no one should have been on B4; so I thought he might be talking to us (this took less than one second) and as I continued to scan ahead I saw a helicopter north bound on runway XY low level. (I believe the helicopter had come from his base eastbound; overflew taxiway A and then turned low level northbound on runway XY).The pilot flying and I both hit the brakes immediately as the helicopter passed in front of us. Probable cause of near collision; ground controller gave a us taxi clearance with runway crossing instructions; the tower controller gave the helicopter a clearance to depart north bound on runway XY and failed to realize we were taxiing.
A Check Airman in a Cessna 172 reported that when as they started to cross a runway; a helicopter flew at low level in front of them causing a NMAC.