  Finding out if neutrinos are Dirac or Majorana particles is known to be
extremely difficult due to the smallness of neutrino mass and the fact that in
the limit $m_\nu=0$ both Dirac and Majorana neutrinos become Weyl particles,
i.e. are indistinguishable. There have been suggestions in the literature that
in the case of processes with production of a neutrino-antineutrino pair (if
neutrinos are Dirac particles) or two neutrinos (if they are of Majorana
nature) quantum statistics may be of help. This is because for Majorana
neutrinos quantum indistinguishability of identical particles requires the
amplitude of the process to be antisymmetrized with respect to the interchange
of the final-state neutrinos, whereas no such antisymmetrization must be done
for Dirac neutrinos. It has been claimed that the resulting differences between
the cross sections for Dirac and Majorana neutrinos persist even for
arbitrarily small but not exactly vanishing neutrino mass. We demonstrate that,
at least in the framework of the Standard Model, this is not the case. We also
give a general proof that within the Standard Model quantum statistics does not
help tell Dirac and Majorana neutrinos apart in the limit of negligibly small
$m_\nu/E$.
