CL65 DSNDING AT 200 FT FOR RWY 22 AT LGA WAS ISSUED GAR BECAUSE OF TFC DEPARTING RWY 31; RESULTING IN AN NMAC.

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WE WERE OPERATING A FLT FROM CVG-LGA. PERFORMED LDA APCH FOR LNDG RWY 22 IN DARK NIGHT VMC. WE WERE CLRED TO LAND ON RWY 22 AT LGA WHILE STILL MORE THAN 5 MI OUT. DURING APCH; A NEW TWR CTLR CAME ON FREQ AND CLRED US TO LAND AGAIN. WE ACKNOWLEDGED THAT XMISSION AND CONTINUED. WHEN WE WERE LESS THAN 2 MI FROM THE RWY 22 THRESHOLD; THE CTLR CLRED A BE1900 TO DEPART ON RWY 31. I REMARKED TO THE FO THAT THAT WOULDN'T WORK; THE SPACING APPEARED INADEQUATE. WHEN WE WERE ABOUT 200 FT ABOVE THE TOUCHDOWN ZONE; THE CTLR INSTRUCTED US TO GO AROUND. WE BEGAN THE GAR IMMEDIATELY; BUT THE OTHER ACFT WAS ALREADY AIRBORNE AND ON A CONVERGING PATH. WE DID NOT TAKE EVASIVE MANEUVERS; BUT PASSED VERY CLOSE BEHIND AND NO MORE THAN 100 FT ABOVE THE OTHER ACFT. AFTER WE WERE CLR OF THE CONFLICT; THE CTLR INSTRUCTED US TO LEVEL AT 1000 FT (ALTHOUGH WE WERE ALREADY AT 1100 FT AND THE MISSED APCH ALT WAS 2700 FT). THIS CAUSED A SMALL; ADDITIONAL THREAT TO THE SAFETY OF THE FLT. MY GUESS IS THAT THE NEW CTLR WAS NOT FULLY AWARE OF THE POS OF THE ACFT BEING HANDLED.