PLT ON THE GND AT AN UNCTLED ARPT CALLS MEM APCH FOR AN IFR CLRNC THEN DEPARTS WITHOUT A RELEASE.

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THE PLT CALLED ON THE GND VIA REMOTE FREQ REQUESTING IFR CLRNC TO RVS (TULSA-RIVERSIDE). ISSUED THE CLRNC WITH THE FIRST ITEM BEING 'HOLD FOR RELEASE.' THE PLT READ BACK THE CLRNC; I TOLD HIM 'READBACK CORRECT; WHICH RWY AND HOW LONG BEFORE YOU'RE READY.' HE REPLIED RWY 35; BUT I DIDN'T HEAR THE TIME AND WASN'T POSITIVE OF THE RWY DUE TO ANOTHER FREQ OVERRIDING HIS REPLY. WITHIN LESS THAN 20 SECONDS OR SO; DURING WHICH I WAS COORDINATING THE USE OF W DEP AIRSPACE FOR; BUT THE RELEASE; I REQUESTED THAT THE PLT VERIFY THE DEP RWY THERE WAS NO REPLY. APPROX 3 MINS LATER THE PLT REPORTED AIRBORNE OFF AWM; AFTER THE INITIAL CONTACT; IN WHICH I ISSUED 'RADAR CONTACT.' I INFORMED THE PLT THAT HE DID NOT HAVE AN IFR RELEASE FROM THE ARPT. HE RETORTED THAT 'THE OTHER GUY' NEVER TOLD HIM TO HOLD. I REPLIED THAT IT WAS INDEED THE FIRST INSTRUCTION GIVEN. THIS OCCURRED DURING A BUSY ARR PUSH AT MEM SO I COULD NOT GIVE MY UNDIVIDED ATTN TO THIS 1 PLT. AFTER REVIEWING THE RULES IN BOTH THE AIM AND THE 7110.65N; I CAME TO THE CONCLUSION THAT MY ERROR LAY IN NOT ISSUING AN 'EXPECT FURTHER CLRNC' TIME; BUT THE PLT'S MISTAKE LAY IN DEPARTING AN ARPT WITHIN THE CLASS B AIRSPACE WITH ONLY AN IFR CLRNC; NOT A RELEASE.