ATCT LCL CTLR RESEQUENCED A DEP CITATION JET BACK TO THE ARPT WITH ANOTHER ACFT ON AN INST APCH; BUT NOT PROVIDING THE REQUIRED SEPARATION CRITERIA.

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I WAS WORKING LCL/GND CTL COMBINED. A COLD FRONT WAS MOVING THROUGH THE AREA. WX WAS IN TRANSITION: VISIBILITY GOOD (10+ MI); CEILING WAS BROKEN 600 FT; ASOS HAD JUST CHANGED TO SCATTERED 600 FT BROKEN 1400 FT; HOWEVER I HAD NOT CHANGED THE ATIS. ACFT X HAD DEPARTED RWY 34. WHEN I INSTRUCTED HIM TO CONTACT DEP CTL; HE INFORMED ME HE NEEDED TO RETURN TO LAND. I WAS AWARE THAT THE ASOS HAD CHANGED; MAKING THE FIELD VFR SO THAT ACFT X COULD BE CLRED FOR A VISUAL APCH RATHER THAN BE VECTORED FOR THE INST APCH. I ASKED IF HE NEEDED ASSISTANCE OR HAD A PROB; AND HE REPLIED NEGATIVE. THE ONLY OTHER TFC WAS CITATION Y ON THE ILS APCH. I ASKED ACFT X IF HE COULD MAKE THE VISUAL APCH; AND HE REPLIED THAT HE THOUGHT HE COULD KEEP THE ARPT IN SIGHT WITH THE CLOUDS; SO I CLRED HIM FOR A VISUAL APCH TO RWY 34. ACFT Y WAS ON A 6 MI FINAL; AND THE CLOUD COVER S OF THE ARPT WAS BROKEN WITH ACFT BREAKING OUT ABOUT 2800 FT MSL ON THE ILS APCH. ACFT X COULD PROBABLY HAVE TURNED BASE AND LANDED AHEAD OF ACFT Y; BUT I WAS NOT SURE HOW MUCH MANEUVERING HE WOULD REQUIRE; SO I ASKED HIM TO EXTEND DOWNWIND; OR MAKE A R 360 DEG TURN TO FOLLOW THE OTHER CITATION. HE (ACFT X) SAID HE COULD MANEUVER TO THE SW OF THE FIELD TO STAY CLR OF CLOUDS. AS HE MANEUVERED; I PERIODICALLY LOST SIGHT OF HIM BEHIND CLOUDS. ON THE D-BRITE SCOPE; I SAW ACFT X TRACKING TOWARD THE FINAL ON A BASE LEG; AND I ADVISED HIM TO CONTINUE CIRCLING; WHICH HE DID. I SAW ACFT X; BUT NOT ACFT Y YET -- THE ACFT WERE ABOUT 1 MI APART; AND THE COLLISION ALERT ACTIVATED. ACFT Y LANDED; ACFT X MANEUVERED AROUND FOR THE BASE LEG BEHIND AND LANDED. SINCE I WAS WORKING LCL CTL; MY THINKING WAS THAT ACFT X WAS IN THE PATTERN (I TREATED HIM AS A VFR RATHER THAN AN IFR ACFT ON A VISUAL APCH) REQUIRING 3 MI SEPARATION UNTIL HE SAW HIS TFC; OR I SAW BOTH. MORE ALERTNESS AND RAPID ASSESSMENT OF THE SIT IS REQUIRED DURING UNUSUAL SITS. INCIDENTALLY; THE REASON ACFT X HAD TO RETURN WAS TO CHK A WARNING LIGHT. HE PROMPTLY DEPARTED AGAIN.