ATX MDT CROSSES RWY WITHOUT AUTH FROM GND CTL.

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I AM AN ATC SPECIALIST AND WAS WORKING GND CTL AT MEMPHIS INTL ARPT DURING LIGHT TFC. WHILE WAITING FOR AN SMT Y; WHO HAD JUST LANDED RWY 27; TO EXIT THE RWY AND CALL; I OBSERVED AN MDT X TAXIING SWBOUND ON TXWY 'S' TOWARD RWY 27. SINCE I WASN'T TALKING TO THE MDT. I ASKED IF ANYONE ELSE IN THE TWR WAS COMMUNICATING WITH HIM. NO ONE WAS. I OBSERVED THE MDT X CROSS RWY 27 AND FOLLOW THE SMT SBOUND ON TXWY C. I MADE A XMISSION 'IN-THE-BLIND' AND MDT X ANSWERED AND ADMITTED THE MISTAKE. THE PLT INFORMED ME HE HAD CALLED 'MEMPHIS GND' TO GO FROM COMPANY RAMP TO HANGAR AND WAS TOLD HE HAD APPROVAL TO DO SO. THE PLT REALIZED THAT THERE MAY HAVE BEEN A PROB WHEN HE SAW THE SMT. HE THEN REALIZED THAT HE HAD BEEN TALKING TO RAMP TWR AND NOT FAA GND CTL. TO PREVENT THIS FROM HAPPENING I WOULD SUGGEST THAT PROCS BE DEVELOPED/ENFORCED THAT REQUIRE A RAMP TWR (OPERATED BY A COMPANY FOR RAMP OPS ONLY) TO IDENT ITSELF AS SUCH ON INITIAL CONTACT. ALSO; DEVELOP STANDARD PHRASEOLOGY FOR ACFT THAT WILL LEAVE THE RAMP AREA AND NEXT ENTER A MOVEMENT AREA THAT IS UNDER FAA JURISDICTION. SUPPLEMENTAL INFO FROM ACN 236341: COPLT: I CALLED COMPANY RAMP CTL TWR TO ADVISE THEM WE WERE ENTERING THE RAMP; ALSO LISTENING TO MEM GND CTL FREQ. OUR FREIGHT WAS OFF LOADED AND WE STARTED #1 ENG TO PREPARE FOR THE TAXI TO HANGAR. I NEGLECTED TO NOTE THAT THE MIKE BUTTON FOR COMPANY WAS STILL SELECTED. XMISSIONS ARE AS FOLLOWS: 'MEMPHIS GND; MDT X ON THE GND RAMP; REPOSITION TO HANGAR. MDT X IS CLRED TO HANGAR.' WE THEN PROCEEDED TOWARDS HANGAR VIA TXWYS S AND C. ABOUT THE TIME WE CROSSED THE HOLD SHORT LINE FOR RWY 27 WE NOTICED AN SMT TAXIING ON RWY 27 THEN TURN L (S ON TXWY C). I THEN MADE ANOTHER XMISSION: 'IS IT OKAY IF MDT X TAXIES DOWN RWY 27 TO TANGO TO HANGAR?' CTLR: 'MDT X CONTACT MEM GND.' AT THE TIME I SAW THE SMT; I KNEW SOMETHING WAS WRONG AND WHEN THE CTLR SAID TO CONTACT GND CTL IT WAS APPARENT THAT I HAD BEEN TALKING TO RAMP; NOT MEM GND. I IMMEDIATELY SWITCHED TO MEM GND AND TOLD THEM WE WERE GOING TO HANGAR AND BRIEFLY EXPLAINED WHAT HAPPENED. THEY TOLD US TO CALL THE TWR. MY MISTAKE WAS NOT ENSURING I HAD THE PROPER MIKE BUTTON SELECTED AND NOT NOTING THE CTLR DID NOT IDENT HIMSELF AS MEM GND. RAMP CTL DIDN'T NOTE THAT I CALLED MEM GND; NOT COMPANY RAMP CTL; AND HE THEN CLRED US TO HANGAR. THE CAPT CONTINUED ACROSS RWY 27 EVEN THOUGH HE SAW THE SMT TAXIING ON RWY 27.