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Distinguishing the Dirac and Majorana nature of neutrinos remains one of themost important tasks in neutrino physics. By assuming that the $\tau^- \to\pi^- \mu^- e^+ \nu$ (or $\bar{\nu}$) decay is resonantly enhanced by theexchange of an intermediate mass sterile neutrino $N$, we show that the energyspectrum of emitted pions and muons can be used to easily distinguish betweenthe Dirac and Majorana nature of $N$. This method takes advantage of the factthat the flavor of light neutrinos is not identified in the tau decay underconsideration. We find that it is particularly advantageous, because of nocompeting 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 ofparticle $X \in \{ e, \mu, \pi, N \}$.

Discovering intermediate mass sterile neutrinos through $\tau^- \to \pi^- \mu^- e^+ \nu$ (or $\bar{\nu}$) decay