  In this paper, we show how a presence of the exotic scalar, tensor weak
interactions in addition to the standard vector-axial (V-A) one may help to
distinguish the Dirac from Majorana neutrinos in the elastic scattering of
(anti)neutrino beam off the unpolarized electrons in the limit of vanishing
(anti)neutrino mass. We assume that the incoming (anti)neutrino beam comes from
the polarized muon decay at rest and is the left-right chiral mixture with
assigned direction of the transversal spin polarization with respect to the
production plane. We display that the azimuthal asymmetry in the angular
distribution of recoil electrons is generated by the interference terms between
the standard and exotic couplings, which are proportional to the transversal
(anti)neutrino spin polarization and independent of the neutrino mass. This
asymmetry for the Majorana neutrinos is distinct from the one for the Dirac
neutrinos through the absence of interference between the standard and tensor
couplings. Additionally, the interference term between the standard and scalar
coupling of the only left chiral neutrinos, absent in the Dirac case, appears.
We also indicate the possibility of utilizing the azimuthal asymmetry
measurements to search for the new CP-violating phases. Our analysis is
model-independent and consistent with the current upper limits on the
non-standard couplings.
