A B737 ON VISUAL APCH RECEIVES A TCASII RA ON FINAL FROM A TFC WATCH HELI AND INITIATES A CLB TO 2300 FT OVER THE ARPT. THE B737 CONFLICTED WITH A LNDG BE55 DIRECTLY OVER THE ARPT AT 2500 FT AND A DEPARTING C550.

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ACR X WAS INBOUND TO RWY 13R AND HAD BEEN ISSUED WINDS AND A LANDING CLRNC. TFC WATCH HELI NGA Y WAS ON THE 'NORMAL' CIRCUIT OVER THE INTERSTATE WHICH RUNS ALMOST PARALLEL TO THE 13L/13R RWYS; S OF THE ARPT; THEN TURNS NW AT THE W CORNER OF THE ARPT. I ISSUED THE HELI TFC TO ACR X AS OFF HIS R; NBOUND AT 1200 FT. THE ALT CHANGED FROM 1100 FT TO 1200 FT AS I WAS ISSUING THE TFC. ACR X REPLIED THAT HE HAD HIM ON TCASII. I LOOKED UP AND THE BOEING WAS IN A DRASTIC CLB. I COULD SEE THE WHOLE UNDERSIDE. THE BOEING CROSSED THE RWY 13R THRESHOLD; ALTHOUGH HE NEVER STATED IT WAS AN RA CAUSED CLB AT APPROX 2200 FT. I WAS ATTEMPTING TO ADVISE REGIONAL (DFW) APCH ABOUT THE BOEING'S GAR. THE ACFT WAS AT 2300 FT. I INSTRUCTED HIM TO DSND AND MAINTAIN 2000 FT. I ISSUED TFC TO THE BOEING ABOUT THE BARON. REGIONAL APCH HAD BARON (Z) NBOUND OVER THE TOP OF RWY 18/36 FOR SEQUENCING TO LAND ON RWY 13L. NORMAL PROC. THE BE55 WAS AT 2500 FT; THE BOEING AT 2300 FT. THE BOEING NEVER REPORTED THE BARON IN SIGHT; BUT (LUCKILY) DID PASS BEHIND HIM. THE BOEING WAS AT 2200 FT AT THE DEP END OF RWY 13R. THAT WAS JUST IN TIME TO TIE A DEPARTING IFR JET OFF OF RWY 13L. ACR X WAS INSTRUCTED TO MAINTAIN VISUAL SEPARATION WITH THE DEPARTING CITATION (A) AND TO CONTINUE ON RWY HDG. THE CITATION WAS CONTINUING OFF RWY 13L; RWY HDG; CLBING TO 5000 FT. AS HE GAINED SPEED AND ALT; HAVING ISSUED HIM NO DELAY CLBING OUT OF 3000 FT; I SWITCHED CITATION TO REGIONAL (DFW) DEP CTL. I COORDINATED WITH REGIONAL APCH AND ISSUED A L TURN TO ACR X FOR L TFC TO RWY 13R. I HAD ALREADY BEEN IN CONTACT WITH THE OVERFLT; BARON; AND HAD ISSUED HIM DSCNT AND A SHORT APCH TO LAND ON RWY 13L. THE 'NORMAL' CLB (MISSED APCH) FOR ACR X WOULD HAVE CLBED HIM DIRECTLY INTO THE INBOUND OVERFLT AT 2500 FT. ALSO; OUR OWN (LIMITED RADAR TWR) RADAR CTLR ALWAYS CLBS ALL OF THE OVERFLTS (ADS-RBD-NBE-TO DOWNTOWN; ETC; ETC) THAT THEY CTL AND CROSS OVER RWY 18/36 N AND SBOUND AT 2000 FT. LUCKILY; THERE WAS NOBODY AT 2000 FT TODAY. I STILL DON'T KNOW IF THE PLT WENT AROUND DUE TO AN 'RA' BECAUSE HE NEVER SAID -- OR BECAUSE HE COULDN'T GET DOWN. IT APPEARED DUE TO THE RA AND WAS VERY CLOSE!!!