The Compact Muon Solenoid (CMS) is one of the general-purpose detectors to be provided for the LHC project at CERN. The design field of the CMS superconducting magnet is 4T, the magnetic length is 12.5 m and the free bore is 6 m. It will produce a magnetic field of 4T in a bore 6m in diameter and 12.5 m long. The coil is wound from 20 high purity aluminium-stabilized NbTi conductors with a total length of 45 km. The main peculiarity of the CMS magnet amont other existing thin detector solenoids is its sandwich-type aluminium-stabilized superconductor. This special feature was chosen in order to have a mechanically self-supporting winding structure. We measured the critical current of all the 21 finished conductors in fields up to 6T using the Ma.Ri.S.A. test facility at INFN-Genova. We compare these results with the critical current of single strands measured by CEA-Saclay, extracted from the conductor after the co-extrusion. A comparison among the measurements provides information about the possible critical current degradation and assures an accurate quality control of the conductor production. We also qualified the method used for making the joints between the layers within a single module and between the five modules and the busbar. Measurements on both round and straight TIG welded samples were carried out, in Genova and at CEA-Saclay, respectively.