TCASII RA AND EVASIVE ACTION CLB DURING A VISUAL APCH TO ARPT MAKES RPTR WONDER AS TO THE VISUAL SEPARATION PROC USED BY ATCT LCL CTLR; AND WHY NO TA ON THE TCASII; ONLY RA.

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AT APPROX PM35L; AFTER HAVING BEEN CLRED FOR A VISUAL APCH TO 17R AT LAREDO; AND DSNDING THROUGH 2400 FT MSL; WE RECEIVED AN RA (RESOLUTION ADVISORY) ON OUR TCAS FOR AN ACFT CLBING; 100 FT BELOW OUR ALT; AND WITHIN OUR '2 MI' RADIUS. WE RECEIVED A TCAS INSTRUCTION TO 'CLB; CLB; CLB'. A CLB WAS INITIATED TO APPROX 2800' MSL. THE LAREDO TWR CTLR THEN ADVISED OF A LIGHT TWIN WHO HAD DEPARTED LAREDO APPROX 4 MINS EARLIER NBND. THIS WAS THE FIRST INFO OR ADVISORY OF THIS TFC. WE WERE NOT ABLE TO VISUALLY CONFIRM THE LOCATION OF THIS TFC; ALTHOUGH THE ACFT STATED AFTERWARD THAT HE HAD US IN SIGHT. UPON COMPLETING THE CLB; THE TCAS MESSAGE WAS 'CLR OF CONFLICT.' WE INITIATED A R TURN IN ORDER TO REALIGN WITH FINAL TO THE RWY; AND ADVISED THEM WE WOULD MAKE A R 270 DEG. THIS PUT US 1/2 MI TO THE R OF THE FINAL APCH PATH. LAREDO THEN ADVISED US TO TURN BACK TO THE S; CROSS OVER THE ARPT MIDFIELD AND ENTER A L DOWNWIND FOR 17R. THE TCAS WAS OPERATIONAL; AND DELIVERED A MESSAGE OF CONFLICTING TFC WHICH WE HAD NOT RECEIVED BY LCL CTLRS. THE ACFT SHOWED UP ON TCAS AS AN RA. WE DID NOT RECEIVE PRIOR WARNING FOR 'TFC; TFC' AS A TA (TFC ALERT); WHICH LEADS US TO BELIEVE THAT PERHAPS THE DEPARTING TWIN HAD JUST THEN TURNED ON HIS TRANSPONDER. OUR PERCEPTION OF THIS SITUATION IS THAT A POTENTIAL CONFLICT WAS AVOIDED BY INITIATING A 'CLB' RESPONSE TO THE TCAS COMMAND. EVEN THOUGH THE OTHER ACFT SAID HE HAD US IN SIGHT; WE DID NOT SEE HIM. THE TWIN ACFT WAS NOT MENTIONED BY THE CTLR UNTIL WE INQUIRED ABOUT THE ACFT IN OUR VICINITY AS DEPICTED ON THE TCAS. IN MY OPINION; A POSSIBLE SERIOUS CONFLICT WAS AVOIDED.