DURING AN ILS APCH; FLC OF AN ACR MLG ACFT TOOK EVASIVE ACTION IN RESPONSE TO A TCASII RA.

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AFTER ASSIGNING FLT AN INTERCEPT HDG AND CLRNC FOR THE ILS 4 APCH TO DEADHORSE; THE CTR CTLR ISSUED TFC AT 11 O'CLOCK AND 5 MI WITH AN UNVERIFIED ALT OF 600 FT. THIS COINCIDED WITH TCASII TFC. AFTER ACKNOWLEDGING THIS; THE CTLR TOLD US TO CONTACT DEADHORSE RADIO. WE CONTACTED RADIO APPROX 2 MI FROM THE FINAL APCH FIX (CIMAS). AFTER OUR CALL TO RADIO; AN ACFT CALLED RADIO AND GAVE THEIR POS AND ALT. THIS RPT WAS CONSISTENT WITH THE TCASII TARGET. AFTER XING THE FINAL APCH FIX; ON GS AND LOC; WE ASKED THE ACFT TO VERIFY THEIR POS AND ALT. THEY COMPLIED AND AGAIN THIS WAS VERIFIED BY THE TCASII. AS WE WERE DSNDING ON THE GS AT APPROX 1300 FT MSL THE TCASII ISSUED A TA; FOLLOWED ALMOST SIMULTANEOUSLY BY AN RA. WE COMPLIED WITH THE RA AND CONFIGURED FOR THE MISSED APCH. WE THEN SPOTTED THE TFC AND VERIFIED THAT THEY HAD US IN SIGHT. THEY CONFIRMED THAT THEY HAD US IN SIGHT AND WERE GOING TO MANEUVER TO THE L TO OVERFLY THE ARPT AND ENTER THE R DOWNWIND TO LAND ON RWY 4. THE TCASII ISSUED A 'CLR OF TFC' ALERT AS THE ACFT WAS MANEUVERING TO THE L IN ORDER TO FLY OVERHEAD THE ARPT. THE TA AND RA AND 'CLR OF TFC' ANNOUNCEMENT OCCURRED IN VERY QUICK SUCCESSION. OUR FLT PASSED APPROX 600 FT HIGHER THAN AND WITHIN APPROX 3/4 OF A MI HORIZLY FROM THE ACFT. THE SEPARATION WAS THE EQUIVALENT TO THE SEPARATION THAT WOULD HAVE OCCURRED DURING LNDG ON PARALLEL RWYS AT A TWR CTLED ARPT. THE WX AT THE TIME OF THIS OCCURRENCE WAS RPTED TO BE CEILING OF 1000 FT AND VISIBILITY OF 7 MI.