FLAT TIRE DURING LNDG PROC CREATES A LOSS OF ACFT CTL AND SUBSEQUENT RWY EXCURSION.

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NORMAL VISUAL APCH TO LNDG. ON TOUCHDOWN ALL SEEMED NORMAL FOR A SECOND OR 2. THEN ACFT STARTED GOING L AND SOON IT BECAME OBVIOUS CAPT DID NOT HAVE FULL CTL OF ACFT. AS WE STARTED GOING OFF L SIDE OF RWY; I CALLED 'R BRAKE; R BRAKE!' HE SAYS ' I AM; I AM.' SLID OFF TO RWY SHOULDER HITTING SOME TAXI AND RWY LIGHTS. WHEN CAME TO STOP ON SHOULDER; INFORMED TWR WE HAD A PROBLEM AND WERE SHUTTING DOWN. DID SO BECAUSE OF ENG VIBRATION. AS I SECURED ACFT; TALKED TO TWR AND STAYED WITH PAX; CAPT EXITED ACFT TO VIEW PROBLEM. HE CAME BACK AND STATED L MAIN GEAR TIRE WAS FLAT. LATER; WE NOTICED DAMAGE TO BOTH PROPS -- PROBABLY FROM STRIKING RWY LIGHTS. ARPT MGMNT AT SCENE WANTED IMMEDIATE REMOVAL OF ACFT SO WE CLRED THIS THROUGH COMPANY AND ACFT WAS TOWED AWAY WITH DOLLY. PICTURES WERE TAKEN PRIOR TO MOVEMENT. TIRE DAMAGE WAS MINIMAL -- DID NOT APPEAR TO BE A BLOWOUT. MAY HAVE SIMPLY BECOME PARTIALLY DEFLATED IN FLT DUE TO PUNCTURE ON TKOF AND THEN COULDN'T HOLD WT OF ACFT. APPEARED. OKAY ON PREFLT AND ACFT HAD MAINT CHK A FEW HRS BEFORE. ADDITIONALLY; LNDG WAS SMOOTH. AS A SIDE NOTE; WE WERE OFF SIDE OF RWY FOR APPROX 45 TO 60 MINS WITH ESSENTIAL BUS ON TO PWR COM RADIO TO TWR. THIS ALSO WOULD HAVE THE COCKPIT VOICE RECORDER PWRED. THIS BEING THE CASE; ANYTHING SIGNIFICANT TO INCIDENT WOULD HAVE BEEN RECORDED OVER. COCKPIT VOICE RECORDERS ARE NEW TO OUR ACFT AND CHKLISTS AND PROCS DO NOT REFLECT THE NEED TO PULL COCKPIT VOICE RECORDER CIRCUIT BREAKER. I THOUGHT OF THIS AT THE TIME; BUT DID NOT WANT IT TO APPEAR AS IF I WAS TAMPERING WITH THE COCKPIT VOICE RECORDER BY PULLING CIRCUIT BREAKER. LATER; AFTER ACFT WAS TOWED TO A HANGAR; COMPANY MAINT DEPT INSTRUCTED US TO PULL COCKPIT VOICE RECORDER CIRCUIT BREAKER; PROBABLY TOO LATE.