ATCT LCL CTLR CLRED AN ACR E120 FOR TKOF ON RWY 36L. ONCE AIRBORNE TWR TOLD FLC TO CALL THE TWR AFTER LNDG AS THEY HAD DEPARTED ON A CLOSED RWY. SUBSEQUENT CONVERSATION WITH TWR SUPVR INDICATED IT WAS THE TWR CTLR'S ERROR.

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TAXIING FOR TKOF AT DFW CONTACTED W SIDE GND CTL. WE WERE TOLD TO HOLD SHORT OF RWY 36R AND CHANGE TO TWR. TWR CTLR INSTRUCTED US TO CROSS RWY 36R AND HOLD SHORT OF RWY 36L. WE READ BACK THE CLRNC AND BEGAN TO TAXI. AS WE WERE XING RWY 36R; TWR ASKED IF WE WOULD BE READY WHEN WE REACHED RWY 36L. WE ACKNOWLEDGED WITH AN AFFIRMATIVE. WE WERE THEN CLRED BY THE TWR TO TKOF ON RWY 36L. WHILE WE WERE IN THE TKOF ROLL WE HEARD A TKOF CLRNC CANCELED FOR ANOTHER ACFT BY THE TWR CTLR. IT WAS NOT FOR US SO WE CONTINUED THE TKOF. ONCE AIRBORNE THE CTLR TOLD US WE HAD JUST DEPARTED OFF A CLOSED RWY WHICH HAPPENED TO BE RWY 36L. HE INFORMED US THAT WE HAD BEEN CLRED OVER TO RWY 31L WITH A FREQ CHANGE TO ANOTHER TWR FREQ. HE THEN ASKED US TO STAND BY FOR THE TWR PHONE NUMBER AND THE SUPVR'S NAME AND WERE INSTRUCTED TO CALL WHEN WE REACHED OUR DEST. UPON ARR AT OUR DEST WE CALLED THE DFW TWR SUPVR WHO HAD ALREADY REVIEWED THE TWR TAPES. HE INFORMED US THAT WE HAD BEEN CORRECTLY CLRED OFF OF RWY 36L AND THAT IT HAD BEEN DEEMED CTLR ERROR. THE SUPVR HAD CITED IMPROPER PHRASEOLOGY BY THE CTLR AS A CONTRIBUTING FACTOR. THE SUPVR TOLD US THERE HAD BEEN A RWY INCURSION DUE TO THE CLOSURE OF THE LAST PART OF RWY 36L. CONTRIBUTING FACTORS TO THIS SIT WOULD BE; 1) NOT BEING INFORMED OF THE RWY CLOSURE; 2) TWR ASKING IF WE WOULD BE READY TO GO UPON REACHING RWY 36L. THIS PUT US IN THE MINDSET THAT WE WOULD BE DEPARTING ON THIS RWY AND ONCE WE WERE CLRED FOR TKOF ON THIS RWY EVERYTHING SEEMED NORMAL.