A BEECH 1900D IN CRUISE DECLARED AN EMER DUE TO GEAR VIBRATION AND POSSIBLE LOSS OF MAINT TIRE ON TKOF.

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DURING TKOF AT ROTATION; ACFT VIBRATED. CHKED INSTS -- ALL NORMAL AND RETRACTED GEAR -- ALSO NORMAL. TOLD DEP CTL WE MAY HAVE HIT SOMETHING AND TO CHK RWY. CONTINUED ON FLT AND WAS NOTIFIED BY CTR CTL IT WAS A TIRE AND IT WAS BEING RUN DOWN TO MAINT FOR IDENT. THE FLT FROM ZZZ TO CMH IS APPROX 35 FLT MINS; SO WE WAITED TO HEAR IF IT WAS OURS OR SOMEBODY ELSE'S. ON DSCNT; ACFT VIBRATED. AS PRECAUTION; DECLARED AN EMER AND LOWERED GEAR EARLY; NOTIFIED COMPANY THROUGH AIR/GND; AND TOLD APCH WE WERE GOING TO DO A FLY-BY TO ASSURE THAT THERE WERE TIRES ON ALL GEAR. THERE WAS AND WE EXECUTED A NORMAL PATTERN AND LANDED. ON SUBSEQUENT WALKAROUND #3 INBOARD TIRE TREAD HAD SEPARATED. MAINT WAS SENT DOWN TO INSPECT AND REPLACE TIRE AND ACFT NACELLE. WE THEN RECEIVED FERRY PERMIT AND BROUGHT ACFT BACK TO ZZZ. SUPPLEMENTAL INFO FROM ACN 515307: IT WAS STILL UNCLR WHETHER THE TIRE DEBRIS CAME FROM OUR ACFT. A BEECH 1900D THAT DEPARTED AFTER OUR ACFT CONTACTED US TO SAY THAT THEY SAW THE TIRE ON THE RWY BUT IT APPEARED TOO LARGE TO COME OFF A BEECH 1900D. THE CAPT DECIDED THAT THE BEST COURSE OF ACTION WOULD BE TO DECLARE AN EMER. I CONCURRED. THE CAPT REQUESTED THAT EMER VEHICLES BE PRESENT AS A PRECAUTIONARY MEASURE. TWR VIEWED ALL TIRES ON MAIN AND NOSE GEAR TO BE PRESENT AND INTACT. AT THIS TIME WE EXECUTED A GAR FOLLOWED BY A NORMAL APCH AND LNDG. ON POSTFLT INSPECTION; I VIEWED THE R INBOARD MAIN TIRE TREAD HAD COMPLETELY SEPARATED FROM THE TIRE ITSELF. THE TREAD WAS NOT PRESENT; HOWEVER; THE TIRE STILL HELD NORMAL PRESSURE. IT WAS NOT FLAT. DURING THE FIRST PREFLT; I NOTICED THAT THE R INBOARD MAIN TIRE APPEARED TO BE NEW. THE PAX WERE NOT AWARE OF ANY IRREGULARITIES. WE FELT THAT BECAUSE THE ACFT CHKED OUT NORMALLY DURING FIRST APCH IT WAS NOT NECESSARY TO ALARM THEM. WE DO NOT HAVE A FLT ATTENDANT ABOARD AND NEEDED TO FOCUS ON OUR COCKPIT DUTIES. WE DID EXPLAIN SIT TO PAX AS THEY EXITED THE ACFT IN COLUMBUS.