The characteristics of the partial nuclear muon capture with massive left-handed Dirac neutrino and relativistic component of the muon wavefunction have been derived. The multipole amplitudes are given as a function of neutrino mass parameter and reduced nuclear matrix elements which are modified by the small component of the muon wavefunction. As an example, the capture rate, asymmetry and polarization of recoil nuclei are investigated in terms of these multipole amplitudes.