  Neutrinos are the only known elementary fermions that can exhibit Majorana
nature. As per the "practical Dirac-Majorana confusion theorem" it is
impossible to distinguish between Dirac and Majorana neutrinos via any
kinematic tests when their masses are very small. However, it is also well
known that Majorana neutrino and anti-neutrino present in the final state must
obey the Fermi-Dirac statistics, irrespective of how small the mass of neutrino
is. We propose a new method to search for Majorana neutrinos by exploiting
their quantum statistical property. We analyse `effective' three-body decays of
the kind $X \to Y \nu \overline{\nu}$ (e.g.\ $X \left[ B^0 \right] \to \pi^+
\big( \to \mu^+ \nu_{\mu} \big) \mu^- \overline{\nu}_{\mu} \equiv Y \left[
\mu^+ \mu^-\right] \nu_{\mu} \overline{\nu}_{\mu}$), with 4-momenta of $X$ and
$Y$ experimentally known, such that the 4-momenta of both neutrino and
anti-neutrino can be deduced. For Majorana neutrinos the distribution of events
in the `effective' Dalitz plot for such a well chosen process would be fully
symmetric under exchange of the neutrino and anti-neutrino. Unlike the
neutrinoless double-beta decay or other lepton-number violating modes, this
distinction between Majorana and Dirac neutrinos survives even in the almost
massless neutrino limit due to the quantum statistical property.
