  In this paper, we analyze the elastic scattering of the muon neutrino beam on
the polarized proton target (PPT), and predict how the existence of
CP-violating phase between the complex vector V and axial A couplings of the
left-chirality neutrinos affects the azimuthal dependence of the differential
cross section. The neutrinos are assumed to be Dirac fermions with non-zero
mass. We show that the azimuthal asymmetry of recoil protons does not depend on
the neutrino mass and does not vanish even if $\beta_{VA} = 0$. The CP-breaking
phase $\beta_{VA}$ could be detected by measuring the maximal asymmetry of the
differential cross section. We also indicate the possibility of using the PPT
to distinguish the detector background from the neutrino interactions. Our
analysis is model-independent and the results are presented in a limit of
infinitesimally small neutrino mass.
