THE TWR ISSUED A TA FOR AN ACFT INBOUND AND FOR THE FLC OF AN EMBRAER E120 TO EXPEDITE THEIR CLB ON DEP. HOWEVER; RIGHT AFTER BEING HANDED OFF TO DEP; THE FLC RESPONDED TO A TCASII TA CAUSING THEM TO STOP THEIR CLB AND MAKE A TURN AWAY FROM THE ONCOMING TFC WHICH THEY HAD VISUALLY SIGHTED.

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WE HAD JUST DEPARTED TLH WHEN TWR TOLD US TO EXPEDITE THE CLB FOR INBOUND TFC LNDG ON RWY 36. WE INCREASED OUR RATE OF CLB; THEN TWR TOLD US TO SWITCH TO DEP. THE RADIO WAS SWITCHED TO THE DEP FREQ AND WITHIN SECONDS; WE RECEIVED A TA. TFC WAS ACQUIRED VISUALLY; IT WAS AT OUR 1-2 O'CLOCK POS AT 600 FT ABOVE OUR ALT. WE STOPPED OUR CLB AT 3000 FT MSL AND BEGAN A L TURN TO GIVE SPACE BTWN TFC. WE NOTICED THE ACFT DSNDING; AND SO WE BEGAN A DSCNT. WE LEVELED OFF AT 2500 FT MSL; THE MINIMUM HORIZ DISTANCE HAD BEEN .6 NM. DISTANCE VERTLY WAS A MINIMUM OF 400 FT. TWR OR DEP NEVER DID POINT OUT THE TFC TO US. THE DEP CTLR WAS ASKED IF HE KNEW ABOUT THE TFC; AND REPLIED THAT HE WAS UNAWARE OF THE TFC UNTIL WE HAD POINTED IT OUT TO HIM. WE WERE TOLD THAT THIS TFC WAS PROBABLY TALKING WITH THE TWR CTLR. WE ASKED THE CTLR IF THERE WAS ANY PROB WITH OUR USING THE EVASIVE ACTION. THE CTLR SAID NO FURTHER PROB WAS CREATED. REST OF THE FLT WAS UNEVENTFUL. WE DID NOTICE; HOWEVER; THAT THE AIRSPACE IN AND AROUND TLH WAS BUSIER THAN NORMAL WITH GA ACFT. APCH/DEP CTLRS HAD A HIGHER THAN NORMAL WORKLOAD DUE TO INCREASED TFC AND MISSED RADIO CALLS.