  Distinguishing the Dirac and Majorana nature of neutrinos remains one of the
most important tasks in neutrino physics. By assuming that the $\tau^- \to
\pi^- \mu^- e^+ \nu$ (or $\bar{\nu}$) decay is resonantly enhanced by the
exchange of an intermediate mass sterile neutrino $N$, we show that the energy
spectrum of emitted pions and muons can be used to easily distinguish between
the Dirac and Majorana nature of $N$. This method takes advantage of the fact
that the flavor of light neutrinos is not identified in the tau decay under
consideration. We find that it is particularly advantageous, because of no
competing background events, to search for $N$ in the mass range $m_e + m_{\mu}
\leqslant m_N \leqslant m_{\mu} + m_{\pi}$, where $m_X$ denotes the mass of
particle $X \in \{ e, \mu, \pi, N \}$.
