HELI DEPARTING SUX ENCOUNTERED MISCOMS WITH ATC.

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I WAS UNDER THE CTL OF SIOUX CITY TWR AND HAD REQUESTED A DEP TO THE N FOLLOWED BY A CLBING L TURN OUT TO 2500 FT AND HEADING 240 DEGS TO NORFOLK; NE. THE CTLR CLRED ME FOR A TKOF FROM TXWY C PARALLEL TO RWY 35 AND INSTRUCTED ME TO MAINTAIN TKOF HEADING AND REMAIN N OF THE CTRLINE OF RWY 35. I ACKNOWLEDGED; TKOF AND CLBED STRAIGHT AHEAD TO 2500 FT. SOON AFTER THE CTLR INSTRUCTED ME TO COMMENCE A L TURN. AWARE OF DEPARTING TFC FROM RWY 31 I COMMENCED A GRADUAL TURN TO THE L TO 240 DEGS KEEPING A LOOKOUT FOR TFC DEPARTING RWY 31. AFTER A COUPLE OF MINS; THE CTLR ASKED ME IF I HAD CROSSED THE CTRLINE OF RWY 31 AND I CONFIRMED THAT I HAD; WHEREUPON HE SAID THAT HIS INSTRUCTIONS HAD BEEN TO KEEP ME NE OF RWY 31 AS HE HAD DEPARTING TFC. I TOLD HIM THAT SINCE HE HAD INSTRUCTED ME TO TURN L; I HAD DONE SO AND CROSSED N OF CTRLINE OF RWY 31. TO THIS HE RESPONDED BY SAYING THAT THE CTRLINE EXTENDED TO THE EDGE OF CLASS D AIRSPACE. NOT WISHING TO GET INTO A DISCUSSION; I APOLOGIZED AND THEN HE TOLD ME TO CHANGE TO ADVISORY FREQ. AT NO POINT DURING THIS WHOLE EPISODE WAS MY ACFT AT RISK OF ENDANGERING OTHER ACFT. I WAS AT ADEQUATE ALT AND HAD ALL THE DEPARTING TFC IN SIGHT. ALSO; NEITHER I NOR THE CREW ON BOARD REMEMBER THE CTLR TELLING ME TO REMAIN CLR OF RWY 31. IT IS CONCEIVABLE; HOWEVER; THAT HE MAY HAVE MEANT RWY 31 AND SAID RWY 35 OR THAT I MIGHT HAVE MISSED THE CALLS. SINCE I WAS CLRED TO COMMENCE A L TURN AND I HAD ALL THE DEPARTING TFC IN SIGHT I WAS NOT OVERLY CONCERNED. THE WORKLOAD OF THE CTLR WAS MODERATE AND MAY HAVE CONTRIBUTED TO THE PROB. MY OWN PERCEPTION OF THIS SIT COULD HAVE ALSO BEEN A FACTOR. IT WAS A CLR CASE OF MISINTERPED COMS. LESSON LEARNED IS TO EXERCISE ADEQUATE CAUTION ESPECIALLY WHEN DEPARTING AIRFIELDS WITH MULTIPLE RWYS. ONE WAY TO DO THIS FOR HELI'S; WOULD BE TO TURN AWAY FROM THE PATTERN; GAIN ALT IN A WIDE CIRCLE AND CROSS MIDFIELD ON DEP HEADING. ALSO; IF IN DOUBT QUERY THE CTLR'S INSTRUCTIONS.