CRITICAL AIR CONFLICT BTWN A DSNDING B737 AND A MANEUVERING CITATION JET AT A LOWER ALT 30 NM W OF ELP; TX; ON A 'LAW ENFORCEMENT MISSION.'

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FIRST LEG OF DAY 3 OF 3-DAY TRIP. FO'S LEG. UP TO THE EVENT; EVERYTHING WAS NORMAL. SKY WAS CLR; VISIBILITY UNLIMITED. WE WERE ON A NORMAL DSCNT PATH INTO EL PASO. THE CLRNC AT THE TIME WAS DSND TO 11000 FT; DIRECT TO NEWMAN VOR. SOMETIME DURING THE DSCNT; WE WERE TOLD TO STOP AT 13000 FT FOR TFC. WE WERE TOLD OF THE TFC; BUT WE DIDN'T SEE IT VISUALLY. AS WE PASSED 14000 FT; WE BOTH CALLED ONE TO GO AND SIMULTANEOUSLY GOT A TCASII ALERT FOLLOWED IMMEDIATELY WITH AN RA TO 'INCREASE VERT DSCNT.' I BEGAN TO CONCENTRATE ON FOLLOWING THE RA GUIDANCE WITH THE CAPT LOOKING FOR TFC. THE RA WAS DIRECTING A DSCNT OF APPROX 4000 FPM. THAT NATURALLY RESULTED IN PASSING OUR ASSIGNMENT ALT OF 13000 FT. I THINK IT WAS AT APPROX 13000 FT; WE GOT THE CLR OF CONFLICT ADVISORY AND BEGAN A DSCNT RECOVERY. I THINK WE DSNDED TO APPROX 12300 FT. AS I BEGAN THE DIVE RECOVERY; I LOOKED UP AND SAW THE TFC IN A SOUTHERLY TURN ABOVE OUR ALT. THE CLOSEST DISTANCE I CAN ESTIMATE WAS APPROX 1/2 MI. WE RPTED THE EVENT TO APCH CTL AND HE SAID THAT HE WAS COLLECTING THE INFO AS WELL. JUDGING FROM THE PROX OF THE ACFT FROM MY PERSPECTIVE; I DON'T THINK THIS IS A NEAR MISS EVENT; BUT AN ALTDEV FROM A TCASII RA EVENT. I FOLLOWED THE TCASII GUIDANCE AND ALTHOUGH IT WAS UNCOMFORTABLE TO INCREASE THE DSCNT AS DIRECTED IT MAINTAINED TFC SEPARATION. UNFORTUNATELY; WE SHOT THROUGH OUR ALT TO DO IT. SUPPLEMENTAL INFO FROM ACN 597447: ELP APCH CLRED US DOWN TO 13000 FT AND INFORMED US OF A CITATION JET AT 12000 FT. I ASSUMED APCH WAS TALKING/CTLING THE CITATION. AT APPROX 14500 FT WE RECEIVED A TFC ALERT FROM TCASII; FOLLOWED BY AN RA AT 14000 FT; 'MAINTAIN DSCNT.' I TOLD APCH OF THE RA AND QUERIED HIM ABOUT THE TFC. THERE WAS NO IMMEDIATE RESPONSE FROM APCH. THE FO WAS FLYING AND DOING A FINE JOB OF FOLLOWING THE RA. WE VISUALLY ACQUIRED THE CITATION AT WHAT LOOKED LIKE OUR ALT AND CONTINUED TO FOLLOW THE RA TO 12500 FT. THE CITATION LOOKED LIKE HE WAS TRYING TO TURN AWAY FROM US; IT WAS NOSE ON AT 1 O'CLOCK POS; AND IN A L TURN. I INFORMED APCH THAT WE HAD BLOWN THROUGH OUR ASSIGNED ALT IN RESPONSE TO THE RA AND NOW HAD THE TFC IN SIGHT. HE THEN INFORMS US THAT HE IS NOT TALKING TO THE CITATION! HE SAID THE CITATION WAS A 'LAW ENFORCEMENT ACFT ON A MISSION.' APCH CLRED US TO 9000 FT. THE REST OF THE FLT WAS UNEVENTFUL.