In this report, results on the calibration process of the Drift Tubes (DT) system of the Compact Muon Solenoid experiment are presented. The full commissioning of the calibration procedure has been deployed in year 2008 with the CMS Computing, Software and Analysis challenge (CSA08), which has tested the full work-flow needed for CMS data-taking during the LHC start-up operations. In autumn 2008, the same Calibration work-flow was applied to a high statistics cosmic ray muon data taking period: the Cosmic Run At Four Tesla (CRAFT) period. The accurate measurement of the main calibration conditions corresponding to the Time Pedestals and the Drift Velocity provide the necessary space-time relationship used in the first stage of the muon local reconstruction