ACR ON A CHARTER FLT FROM AN UNCTLED ARPT TAKES OFF WITHOUT A RELEASE FROM ATC.

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AS AN ACR; WE ARE MOST FAMILIAR WITH PART 121 OPS UNDER IFR FLT PLANS AT CTLED ARPTS. MY FO AND I WERE DOING A CHARTED 121 SUPPLEMENTAL OUT OF UNCTLED ARPT. I WAS OUTSIDE THE ACFT WHEN HE PICKED UP OUR IFR CLRNC. APPARENTLY WE SHOULD HAVE CALLED FOR OUR RELEASE (IFR) BEFORE DEPARTING THE ARPT. INSTEAD WE MADE NORMAL RADIO CALLS ON THE CTAF AND DEPARTED THE ARPT. OUR INITIAL ALT WAS 3000 FT MSL. ON CLBOUT THE FO CALLED HOUSTON DEP WITH OUR ALT WE WERE CLBING THROUGH AND THE ALT WE WERE CLRED TO. THE DEP CTLR ASKED US TO IDENT. HE ASKED IF WE CALLED FOR A RELEASE. WE REPLIED NO. THE DEP CTLR CLRED US ON COURSE AND CLRED US TO CLB TO 10000 FT MSL. THE FO APOLOGIZED. THE DEP CTLR SAID 'NO PROB -- JUST DON'T DO IT AGAIN.' I SHOULD HAVE KNOWN BETTER THAN TO DEPART WITHOUT CALLING FOR RELEASE. POSSIBLY BOTH CREW MEMBERS SHOULD BE PRESENT WHEN CALLING FOR A CLRNC. IT MAY BE A GOOD IDEA FOR THE TRAINING DEPT TO TOUCH ON THIS ITEM DURING RECURRENT OR INITIAL. EXTRA DILIGENCE WHEN OPERATING OUTSIDE NORMAL CIRCUMSTANCES.