CARJ CREW HAD A TCASII EVENT WITH A GRUMMAN ACFT IN OMA CLASS C AIRSPACE.

Narrative

POSSIBLE NMAC. OMA DEPARTING RWY 36. CLRNC WAS TO LEVEL AT 3000 FT FOR TFC. AUTOPLT WAS ON. HANDED OFF TO DEP CLBING THROUGH 2000 FT; WE LEVELED AT 3000 FT. DEP ISSUED TFC OFF OUR R AT 3500 FT AND CLBING. WE RPTED VISUAL ON THE GRUMMAN ACFT. OUR TCASII SHOWED TFC +500 FT; NOT CLBING. LATERAL SEPARATION WAS CLOSING. AUTOPLT WAS DISCONNECTED. (IT APPEARED THAT THE GRUMMAN ACFT WAS SKUD RUNNING -- CLOUD DECK WAS JUST ABOVE THE OTHER ACFT.) ATC ISSUED A VISUAL CLB REF; THAT ACFT; AND R TURN ON COURSE. TCASII ISSUED A COMMAND TO CLB. WE DID NOT. A CLB WOULD HAVE PUT US ON A COLLISION COURSE WITH THE OTHER ACFT. WE STARTED TO BANK L AND DSND. TCASII ISSUED 'DSND; DSND NOW;' WITHIN SECONDS 'MAINTAIN VERT SPD' AND 'CLR OF CONFLICT.' THERE WAS NO FURTHER XMISSION WITH ATC UNTIL CONFLICT WAS CLRED AND THOUGHT GATHERED. OUR MANEUVERING OF THE ACFT WAS SLIGHT. LATER; ATC WAS QUESTIONED IF ANY OTHER ACFT WERE IN THE AREA. THERE WAS NONE. OUR PAX COMMENTED TO OUR FLT ATTENDANT ON THE CLOSE PROX OF THE OTHER ACFT. BROKEN CLOUD DECK MAY HAVE PLAYED A PART. TCASII ISSUING A CLB WAS NOT EXPECTED. A DSCNT IS WHAT WAS ANTICIPATED. IOE WAS IN PROGRESS. LCL CTLR WAS WORKING CLRNC; GND AND TWR. TCASII WAS WRITTEN UP UPON OUR ARR AT DEST.