B757 CREW LNDG RWY 31 AT LGA WERE UNABLE TO COMPLY AS INSTRUCTED TO TURN OFF AT TXWY S OR R AND CROSSED RWY 04 WITH TFC ON TKOF ROLL.

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WE WERE LNDG ON RWY 31 AT LGA -- VFR -- UNEVENTFUL LNDG. ON ROLLOUT TWR REQUESTED WE EXIT AT SIERRA (S) OR ROMEO (R) WHICH IS BEFORE RWY 4/22. CAPT DID NOT HEAR REQUEST. FO ACKNOWLEDGED TWR AND TOLD CAPT THEY WANT US TO EXIT HERE AT 'S' OR 'R.' CAPT DETERMINED ACFT HAD NOT SLOWED TO SAFE TAXI SPEED AND DECIDED TO CROSS RWY 4/22 AND EXIT AT AA. FO INFORMED TWR IMMEDIATELY OF OUR INTENTIONS. TWR ROGERED US AND THEN TOLD ACFT ON RWY 04 TO CANCEL TAKEOFF CLRNC AND EXIT RWY. OTHER ACFT HAD JUST STARTED ITS TKOF ROLL. LGA DOES NOT HAVE LAND AND HOLD SHORT PROCEDURES AND TWR SHOULD NEVER ASSUME AN ACFT WILL MAKE A SHORT ROLLOUT AND CLR FOR THEIR CONVENIENCE. ACFT ON RWY 04 SHOULD NOT HAVE BEEN CLRED FOR TAKEOFF UNTIL OTHER ACFT HAD CLRED THE RWY. CALLBACK CONVERSATION WITH RPTR REVEALED THE FOLLOWING INFO: CAPT WAS NOT SURE IF THE FO HAD MERELY RESPONDED WITH 'ROGER' TO THE CTLR'S INSTRUCTION TO TURN OFF AT TXWY S OR R. HE SAID IT WAS DARK AND HE WAS NOT VERY FAMILIAR WITH THE TXWY LOCATIONS. HE SAID THE ACFT ON RWY 04 STARTED TO ROLL FOR ONLY A VERY SHORT DISTANCE AND WAS NOT A PROB. IT WAS EITHER AN ATR42 OR AN ATR72.