B737-800 CREW HAD A TXWY INCURSION AT LGA.

Narrative

OUR FLT WAS CLRED TO TAXI FROM PARKING TO RWY 31 VIA 'TXWY AA; HOLD SHORT RWY 22 ON TXWY P.' I COPIED THIS INTO THE FMC SCRATCH PAD AND READ BACK THE CLRNC. AS WE NEARED TXWY P; ATC CALLED AND SAID THAT WE WERE CLRED TO CROSS RWY 22 AT TXWY P. I READ BACK THE CLRNC AND AGAIN COPIED IT DOWN INSIDE THE COCKPIT. WHEN I LOOKED UP FROM DOING THIS; I REALIZED THAT WE WERE PAST TXWY P. I IMMEDIATELY INFORMED THE CAPT; WHO INITIATED A HARD R-HAND TURN BACK TOWARDS TXWY P. BEING UNSURE OF OUR EXACT POS. I ADVISED THE CAPT TO STOP THE ACFT. I RADIOED ATC THAT I THOUGHT WE HAD PASSED TXWY P. ATC ADVISED US THAT WE APPEARED TO BE ON TXWY P; AND WERE CLRED TO CONTINUE TAXIING ACROSS RWY 22 TO RWY 31. DURING THE TURN BACK TO AND THE RETURN TO TXWY P; I BECAME CONCERNED ABOUT OUR PROX TO THE TXWY MARKINGS/LIGHTING; WHICH I COMMUNICATED TO THE CAPT. AS A PRECAUTION; WE HAD OUR AIRLINE MAINT INSPECT THE ACFT. MAINT RPTED TO US THAT THERE WAS NO DAMAGE; AND WE WERE OK TO PROCEED; WHICH WE DID. I FEEL THAT THIS OCCURRED BECAUSE OF THE USUAL DIFFICULTIES ASSOCIATED WITH TAXIING AT NIGHT; COMPOUNDED BY THE FACT THAT ATC ISSUED A REVISED CLRNC TO US; JUST PRIOR TO WHEN WE NEEDED TO INITIATE A TURN. MY HAVING TO LOOK INSIDE TO COPY THIS CLRNC HAMPERED MY ABILITY TO BACK UP THE CAPT'S TURN.