We report on a study of 495 ± 32 ν μ -induced and 285 ± 29 ν μ- induced prompt opposite-sign dimuon events, obtained in the CERN Super Proton Synchrotron (SPS) horn-focused beam, using the CHARM neutrino detector. Prompt events are selected using the observed distribution of the distance between the two muons at the vertex. The observed increase of the ratio of prompt dimuon to single muon events with E vis is compatible with the expected behaviour for charm quark production and decay. Assuming the GIM mechanism, we fond a strange-sea contribution of 0.050 ± 0.015, in agreement with our previous result not involving the charm-changing currents. In the same sample we observed 74 ± 17 ν μ -induced and 52 ± 13 ν μ- induced prompt same-sign dimuon events. On the basis of their kinematics, these events can be well described as being of hadronic origin. The ratios μ −μ −/μ −μ + and μ +μ +/μ +μ − are found to be 0.14 ± 0.04 (stat.) ± 0.03 (syst.) and 0.18 ± 0.06 (stat.) ± 0.03 (syst.), respectively. The observed ratio σ(μ +μ +) σ(μ −μ −) = 0.50 ± 0.20 is compatible with the ratio of the single-muon charged-current cross sections, σ( ν μ N → μ + X) σ(ν μ N → μ − X) = 0.498 ± 0.019 .