  The Majorana versus Dirac nature of neutrinos remains an open question. This
is due, in part, to the fact that virtually all the experimentally accessible
neutrinos are ultra-relativistic. Noting that Majorana neutrinos can behave
quite differently from Dirac ones when they are non-relativistic, we show that,
at leading order, the angular distribution of the daughters in the decay of a
heavy neutrino into a lighter one and a self-conjugate boson is isotropic in
the parent's rest frame if the neutrinos are Majorana, independent of the
parent's polarization. If the neutrinos are Dirac fermions, this is, in
general, not the case. This result follows from CPT invariance and is
independent of the details of the physics responsible for the decay. We explore
the feasibility of using these angular distributions -- or, equivalently, the
energy distributions of the daughters in the laboratory frame -- in order to
address the Majorana versus Dirac nature of neutrinos if a fourth, heavier
neutrino mass eigenstate reveals itself in the current or next-generation of
high-energy colliders, intense meson facilities, or neutrino beam experiments.
