A PA-30 OPERATING UNDER VFR; OVERSHOT CLRNC ALT RESULTING IN A B737-300 TCASII RA. FLC COMPLIED WITH RA.

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CMH DEP CTL (125.95) ISSUED 'TFC 12 O'CLOCK; 5 NM; CLBING TO 9500 FT; A TWIN COMMANCHE.' ON TCASII; THE TFC APPEARED AT 12 O'CLOCK; 5 NM; 300 FT BELOW AND INDICATING A CLB; THEN AT 400 FT BELOW. A TCASII RA RESULTED; SHOWING A VERT CLB BTWN 1500-2000 FPM. THE CAPT (PNF) HAD INITIALLY REQUESTED A SEPARATION VECTOR AND DEP CTL ISSUED A HDG OF 230 DEGS AT THE SAME TIME AS THE TCASII RA OCCURRED; THE FO (PF) DISCONNECTED THE AUTOPLT AND AUTOTHROTTLE AND INITIATED A CLBING L TURN TO COMPLY. ACFT CLBED TO 10600 FT; ATC NOTIFIED OF DEV AND RA. ONCE CLR OF CONFLICT; DSNDED BACK TO 10000 FT ASSIGNED AND CLRED DIRECT TO DAY. SIT COULD HAVE BEEN PREVENTED BY ATC WITH AN EARLIER VECTOR TO THE L TO AVOID THE APCHING TFC. SUSPECT THAT THE TWIN COMMANCHE OVER SHOT HIS LEVEL OFF ALT THEN CORRECTED BACK. ONCE AGAIN TCASII PROVED INVALUABLE IN EXPANDING SITUATIONAL AWARENESS AND INCREASING THE SAFETY OF FLT MARGIN. SUPPLEMENTAL INFO FROM ACN 306486: AFTER A MONITORED CLB; AND WHEN CLR OF TFC; WE DSNDED BACK TO 10000 FT.