NMAC OF LTT AND SMA ON APCH AND BOTH CLRED TO LAND ON INTERSECTING RWYS.

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WE RECEIVED LNDG CLRNC FOR RWY 14R AT CMI. ANOTHER ACFT WAS CLRED TO LAND ON RWY 22R. BECAUSE OF THIS; BOTH MY FO AND I WERE SCANNING FOR THE OTHER ACFT. THE LCL CTLR'S REMARKS BEGAN TO INDICATE A CONFLICT WAS IN THE MAKING. THE LCL CTLR DID NOT EXCHANGE TFC INFO BTWN ACFT; BUT THE OTHER PLT WAS TOLD BY THE CTLR; HE MIGHT HAVE TO GAR. AS OUR ACFT CROSSED THE LNDG THRESHOLD OF 14R; MY FO SAID HE HAD THE OTHER ACFT INSIGHT. IT THEN APPEARED TO ME AT APPROX 10 O'CLOCK POS TO US AT APPROX OUR ALT. THE OTHER PLT ASKED IF HE SHOULD GAR. THE LCL CTLR ISSUED 'GAR' TO THE OTHER ACFT -- A SMA. WE TOUCHED DOWN IN THE TOUCHDOWN ZONE. I HAD BEEN UTILIZING THE VASI TO THE RWY. THE OTHER ACFT DISAPPEARED AT OR SHORTLY THEREAFTER TOUCHDOWN AT THE TOP OF MY CTR WINDSHIELD; I ESTIMATE NO HIGHER THAN 200 FT AGL. AS WE PASSED THROUGH THE INTXN OF 14R AND 22R; I NOTICED MY FO LOOKING ALMOST STRAIGHT UP THROUGH HIS SIDE DU. WINDOW. I ASSUMED TO MAINTAIN VISUAL CONTACT WITH THE OTHER ACFT. THIS WAS AN UNSAFE OP CONDUCTED BY CMI ATCT. THE TWR SUPVR EXPLAINED DURING A PHONE CALL SHORTLY THEREAFTER; NO SEPARATION CONFLICT EXISTED BECAUSE THE LCL CTLR ISSUED GAR INSTRUCTION BEFORE THE OTHER ACFT CROSSED IT'S LNDG THRESHOLD. I DO NOT AGREE WITH THAT. THE INSTRUCTIONS WERE ISSUED AFTER I FIRST VIEWED THE OTHER ACFT. IT WAS AT MY 10 O'CLOCK POS. THE LCL CTLR HAD NO PLAN. A CORRECT PLAN OF ACTION SHOULD HAVE BEEN FOR EITHER OR BOTH ACFT TO TURN AWAY FROM EACH OTHER FOLLOWED BY CLB INSTRUCTIONS; LONG BEFORE THEY CROSSED THE ARPT BOUNDARY INBOUND TO LAND. TIME AND ROOM TO MANEUVER STILL EXISTED. THERE WAS NO WAY OUT. HAD THE OTHER ACFT NOT BEEN ABLE TO GAR; OR WE HAD TO GAR; WE SURELY WOULD HAVE HAD A MIDAIR COLLISION; OR MY ACFT MIGHT HAVE STRUCK THE GND DURING AN EVASIVE MANEUVER. I UNDERSTAND THIS IS NOT AN UNCOMMON SITUATION AT CMI -- THE CROSS RWY CONFLICT. SOMETHING MUST BE DONE!!!!