B727 AFTER TKOF FROM RWY 4L ACFT HAD LESS THAN LEGAL SEPARATION FROM ACFT ON GAR FROM RWY 4R AT JFK.

Narrative

DEPARTING JFK ON RWY 4L THE SID CALLED FOR A TURN TO 90 DEGS ON DEP UP TO 3000 FT OR 5000 FT. AS WE WERE ROLLING ON RWY 4L FOR TKOF WE HEARD AN ACFT ON APCH TO RWY 4R STATE HE WAS GOING AROUND BECAUSE OF AN UNRELIABLE LOC SIGNAL. WE SAW THE SAME ACFT CLOSING ON THE TCASII. THE GAR ACFT WAS NOW AT OUR ALT. WE LEVELED AT 1500 FT AND TURNED L TO 360 DEGS. THE 1ST RESOLUTION INSTRUCTIONS WE RECEIVED FROM JFK TWR WERE NOT GIVEN UNTIL AFTER WE HAD LEVELED AT 1500 FT AND TURNED TO 360 DEGS. TWR TOLD US TO TURN TO 360 DEGS. I INFORMED THEM WE HAD ALREADY DONE THAT AND WE WERE LEVEL AT 1500 FT. IF IT WERE NOT FOR THE TCASII WE MAY HAVE HAD A MIDAIR FOR THE FOLLOWING REASONS. 1) THE SID DICTATES FLYING THROUGH THE PATH OF THE PARALLEL ACFT'S APCH. 2) THE CTLR WAS EITHER UNABLE TO ISSUE ALTERNATE INSTRUCTIONS OR WAS UNAWARE OF THE CONFLICT. THESE PROCS THAT REQUIRE CTLR CONFLICT RESOLUTION MUST BE STOPPED. WE NARROWLY GOT AWAY THIS TIME. THE CAPT AND I WERE THE ONLY ONES ACTING TO AVERT DISASTER.