A VFR PA28 DEP CONFLICTS WITH AN INBOUND PA34 ON A PRACTICE IFR APCH APPROX 5 MI FROM THE ARPT. THE OUTBOUND ACFT WAS CHANGED TO APCH CTL FREQ AND THE INBOUND PA34 WAS JUST SWITCHED TO TWR FREQ. NO TA'S WERE ISSUED.

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ACFT #1 INBOUND TO BIS ON THE ILS RWY 13 APCH. ACFT #1 IS VFR; HOWEVER; IS ON A VFR PRACTICE APCH SO IS PROTECTED LIKE AN IFR. ACFT #2 DEPARTS RWY 13 AT BIS WITH A L TURN ON COURSE TO THE NW PRACTICE AREA. I SEE THAT TFC NEEDS TO BE ISSUED TO THE 2 ACFT SO I SHIP ACFT #2 TO DEP FOR HIS RADAR ADVISORIES. I SHIPPED ACFT #2 BECAUSE I DETERMINED THE CONFLICT WAS GOING TO TAKE PLACE OUTSIDE OF MY AIRSPACE (OUTSIDE 5 MI). I DID NOT KNOW; HOWEVER; THAT THE APCH CTLR HAD ALREADY SHIPPED ACFT #1 TO MY FREQ. EITHER ACFT #1 DID NOT CHK ON OR I DID NOT HEAR HIM CHK ON. I ASSUMED THAT THE APCH/DEP CTLR WAS ISSUING TFC TO BOTH ACFT. THE NEXT XMISSION I HEAR IS ACFT #1 ASKING WHY HE WAS NOT TOLD ABOUT ACFT #2 THAT JUST FLEW OVER HIM. I FELT HORRIBLE. ALL I COULD TELL HIM WAS THAT I DIDN'T THINK HE WAS ON MY FREQ AND APOLOGIZE FOR THE MISTAKE. THE 2 RADAR TARGETS WERE RIGHT ON TOP OF EACH OTHER AND I AM GUESSING THAT THEY WERE LESS THAN 300 FT APART VERTLY. CAUSES: ME ASSUMING THAT THE OTHER CTLR WAS WORKING IT OUT. I SHOULD HAVE MADE SURE. ALSO; THE OTHER CTLR WAS TRAINING SO MAY NOT HAVE SEEN THE CONFLICT WAS GOING TO TAKE PLACE IN HIS AIRSPACE. HE SHOULD HAVE KEPT ACFT #1 AND ISSUED TFC; BUT BECAUSE HE DIDN'T; I SHOULD HAVE MADE SURE (DON'T ASSUME) TFC WAS EXCHANGED BTWN BOTH ACFT. ANOTHER PAIR OF EYES IN THE CAB WOULD HAVE BEEN WONDERFUL.