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A detailed analysis of the rare $\ensuremath{\tau}$ decay via $\ensuremath{\tau}\ensuremath{\rightarrow}\ensuremath{\mu}e\overline{e}$ and $\ensuremath{\tau}\ensuremath{\rightarrow}\ensuremath{\mu}\ensuremath{\mu}\overline{\ensuremath{\mu}}$ in the string models with ${\mathrm{E}}_{6}$ symmetry is reported. It is found that $\ensuremath{\Gamma}(\ensuremath{\tau}\ensuremath{\rightarrow}\ensuremath{\mu}e\overline{e})\ensuremath{\sim}(6\ensuremath{-}7)\ensuremath{\Gamma}(\ensuremath{\tau}\ensuremath{\rightarrow}\ensuremath{\mu}\ensuremath{\mu}\overline{\ensuremath{\mu}})$ and these rates are in general about 1000 times less than that of $\ensuremath{\Gamma}(\ensuremath{\mu}\ensuremath{\rightarrow}e\ensuremath{\gamma})$. It is also found that the outgoing muon in $\ensuremath{\tau}\ensuremath{\rightarrow}\ensuremath{\mu}e\overline{e}$ …