B727 WAS GIVEN CLRNC TO 'TAXI TO THE GATE' BY SAT GND CTL. TWR LCL CTLR WAS NOT AWARE THAT THIS CLRNC HAD BEEN GIVEN.

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WE RECEIVED A CLRNC FOR A VISUAL APCH TO RWY 3 AT SAT BY THE TWR. WE LANDED UNEVENTFULLY ON RWY 3 AND TAXIED CLR AT THE END OF THE RWY (TXWY N). TWR TOLD US TO TAXI ON TXWY N AND HOLD SHORT OF RWY 12L. THE FO ACKNOWLEDGED AND THE CREW PERFORMED THE AFTER LNDG CHK. JUST PASSING TXWY T WHILE STILL ON TXWY N; THE FO CALLED GND CTL ON 121.9 AND ASKED IF FLT XXX WAS CLRED TO CROSS RWY 12L. AS THE FO CALLED FOR CLRNC TO CROSS RWY 12L; THE CAPT (MYSELF) WAS IN THE PROCESS OF SLOWING THE ACFT TO STOP AND HOLD SHORT OF RWY 12L. GND CTL RESPONDED WITH A CLRNC TO TAXI TO OUR GATE; WHICH REQUIRED US TO CROSS RWYS 12L&R. NEAR OUR GATE; GND GAVE US THE TWR PHONE NUMBER AND ASKED US TO CALL THEM AFTER WE PARKED THE AIRPLANE. TWR IN THE PHONE CONVERSATION SEEMED TO THINK THAT WE CROSSED RWY 12L WITHOUT A CLRNC. THE TWR SUPVR REVIEWED THE TAPES AND TOLD US THAT; IN FACT; WE DID HAVE A CLRNC. I ASKED IF THERE WAS ANY PROB FOR US AND THE TWR SUPVR SAID NO. THE CREW OF FLT XXX NEVER FELT THAT ANYTHING WAS AMISS OR UNUSUAL UNTIL TWR ASKED US TO CALL THEM. PERHAPS GND CTL AND TWR WERE NOT COMMUNICATING WELL.