CTLR PUT ACR INTO TKOF POSITION WITH GA TWIN ON SHORT FINAL. GA ACFT MADE GO AROUND IN CLOSE PROX TO THE ACR. OPERATIONAL ERROR.

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I WAS WORKING LCL CTL. WHEN GA TWIN X CALLED THE TWR; I ADVISED THE ACFT TO SQUARE HIS TURN TO FINAL AND REDUCE SPD SO THAT I COULD GET DEPS OUT BEFORE HIS ARR. THE ACFT AGREED AND I ISSUED THE WIND AND ADVISED HIM TO CONTINUE TO RWY 36R. LATER AFTER ONE JET HAD DEPARTED RWY 36R PRIOR TO ACFT X ARR; ACR Y ADVISED HE WAS READY. I CHKED THE TCDD AND ACFT X WAS ON ABOUT A 2 1/2 MI FINAL I LOOKED OUT THE WINDOW AND DID NOT SEE ACFT X. I TOLD Y TO TAXI INTO POS AND HOLD. SHORTLY AFTER I ISSUED THE TAXI INSTRUCTION TO ACR Y; ACFT X ADVISED THAT Y WAS PULLING ON THE RWY IN FRONT OF HIM; AND THEN ADVISED HE WAS GOING AROUND. I AGREED AND ISSUED 'ACFT X GO AROUND.' ACFT X WAS STILL ON ABOUT 1/3 MI FINAL. X RETRACTED HIS GEAR AND STARTED TO GO AROUND. I THEN TOLD X TO ENTER RIGHT TFC AND CLRED TO LAND RWY 36R. I ALSO TOLD X IT WAS MY FAULT HE HAD TO GO AROUND AND THANKED HIM FOR THE HELP. SINCE THAT DAY; I HAVE BEEN ADVISED THAT ACR Y FELT THAT ACFT X OVERFLEW HIS ACFT AT A LOW ALT. I ADMIT THAT I DID NOT WATCH THIS MANEUVER ALL THE WAY THROUGH SINCE I HAD OTHER DUTIES AS LCL CTLR. IT APPEARED TO ME THAT ACFT X NEVER OVERFLEW ACR Y; BUT PASSED JUST OFF HIS RIGHT AS Y HAD ENTERED THE RWY FROM X'S LEFT. I HAVE SINCE BEEN ADVISED TO BE MORE CAREFUL AND FORGET IT. ANALYST NOTE: TCDD IS TWR CAB DIGITIZED DISPLAY.