AN AIR CARRIER CLRED TO CROSS RWY 04 AT LGA; NY; OBSERVES ANOTHER AIR CARRIER ON ITS TAKE OFF ROLL ON RWY 04. THE DEPARTING ACFT PASSED IN FRONT OF THE TAXIING ACFT 10 TO 20 FT IN THE AIR.

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WE WERE TAXIING OUT OF THE LGA RAMP AREA FOR DEP. WE WERE ON TXWY E AND WERE INSTRUCTED BY GND CTL TO HOLD SHORT OF RWY 04. WE ACKNOWLEDGED AND HELD SHORT OF RWY 04. WE WERE THEN TOLD BY LGA GND TO CROSS RWY 04 TURN R ON TXWY CC AND TAXI TO RWY 13. JUST AS THE CAPT RELEASED THE BRAKES AND STARTED TO ROLL TOWARDS THE HOLD SHORT LINE OF RWY 04; WE LOOKED TO OUR L AND SAW A DASH 8 BEGINNING HIS TKOF ROLL ON RWY 04. THE CAPT IMMEDIATELY STOPPED THE ACFT SHORT OF RWY 04. THE DASH 8 ROTATED AND CROSSED IN FRONT OF OUR NOSE AT APPROX 10-20 FT AGL. I THEN GOT ON THE RADIO (GND) AND ASKED 'WHAT'S HE DOING?' THE GND CTLR THEN RESPONDED 'HOLD SHORT.' AFTER THE DASH 8 WAS AIRBORNE WE WERE AGAIN CLRED TO CROSS RWY 04 AND TAXI TO RWY 13. THE FLT COMMENCED WITHOUT INCIDENT. CALLBACK CONVERSATION WITH RPTR REVEALED THE FOLLOWING INFO: THE RPTR SAID THAT TFC WAS MODERATE DURING THE INCIDENT. THE TWO ACFT INVOLVED WERE ON SEPARATE FREQUENCIES. GND CTL GAVE THE CROSSING CLRNC. APPARENTLY TWR GAVE THE TAKE OFF CLRNC. THIS IS A COMMON USE OF THE FREQUENCIES AND A STANDARD TAXI RTE TO RWY 13. THERE WAS NO FURTHER COMMENT FROM GND OTHER THAN A HOLD SHORT WHEN QUESTIONED. THE ROTATION POINT OF THE DEPARTING ACFT WAS BETWEEN TXWY D AND E. THE ACFT WAS ABLE TO STOP BEFORE CROSSING THE HOLD SHORT LINE WITH AN ESTIMATED DISTANCE OF 30 FT SEPARATION BETWEEN THE NOSE AND THE PASSING ACFT WHO WAS 10 TO 20 FT IN THE AIR. SUPPLEMENTAL INFO FROM ACN 555802: LGA WAS IN THE PROCESS OF CHANGING DEPS FROM RWY 04 TO 13. THE GND CTLR TOLD US TO CROSS RWY 04 AND TURN R ON DOUBLE CHARLIE. I LOOKED TO MY L TO CLR THE AREA AND I SAW A DASH 8 WITH THE LNDG LIGHTS ON AND WHAT APPEARED TO BE A TAKEOFF ROLL ON RWY 04. I IMMEDIATELY STOPPED SHORT OF THE HOLD LINE. THE DASH 8 PROCEEDED DOWN THE RWY AND WAS ABOUT 5-10 FT IN THE AIR AS IT PASSED OUR NOSE. GND CTL SAID; 'HOLD SHORT OF RWY 04.' THE DASH 8 WAS ALREADY PAST OUR NOSE BY THEN. THIS HIGHLIGHTS THE POINT THAT WE NEED TO BE VERY CAUTIOUS AND AWARE OF WHAT IS GOING ON WHEN CROSSING A RWY. ESPECIALLY DURING RWY CHANGES; AND WHEN YOU ARE NOT ON THE SAME FREQUENCY AS THE ACFT ON THE RWY.