  In this paper a scenario admitting the participation of the exotic
right-handed scalar $S_{R}$ coupling in addition to the standard left-handed
$(V, A)_{L}$ couplings in the low energy neutrino-electron scattering is
considered. The main goal is to show how the presence of the right-handed
neutrinos in the $(\nu e)$ scattering changes the laboratory differential cross
section in relation to the Standard Model prediction. We consider the $(\nu e)$
process at the level of the four-fermion point interaction. Muon-neutrinos are
assumed to be massive and to be polarized Dirac fermions. In the laboratory
differential cross section the new interference term between the the standard
$V_{L}$ coupling of the left-handed neutrino and exotic $S_{R}$ coupling of the
right-handed neutrino appears which does not vanish in the limit of massless
neutrino. This new contribution, including the information about the transverse
neutrino polarization, generates the azimuthal assymetry in the angular
distribution of the recoil electrons. This regularity would be the proof of the
presence of R-handed neutrinos in the $\nu e$ scattering.
