  In this paper, we analyze the polarized muon decay at rest (PMDaR) admitting
the non-standard V+A interaction in addition to the standard V-A interaction.
We show that the angle-energy distribution of Dirac muon neutrinos is sensitive
to the interference terms between the standard V-A coupling of left-chirality
muon neutrino and exotic V+A coupling of right-chirality one, which are
proportional to the transverse components of muon neutrino spin polarization.
The interferences do not vanish in a massless limit and include the relative
phases to test the CP violation (CPV). It allows to calculate a neutrino flux
for an assumed configuration of detector in the case of SM prediction, and the
upper limits on the neutrino flux for the left-right muon neutrino mixture. We
also demonstrate that the effects of neutrino mass and mixing are tiny
corrections and can be omitted. The most important conclusion is that even in
the massless limit, there are physical effects connected with the mixture of
left- and right-handed helicity components in a spin 1/2 quantum state, when
exotic interaction V+A is admitted contrary to the electron observables, where
all the possible interferences vanish.
