  The flavor-violating decay of a new neutral massive gauge boson
$Z^\prime\to\mu e$ is analyzed in the context of extended models, in which this
particle emerges. By means of the analysis of the $\mu\to e\gamma$ decay,
$\mu-e$ conversion process in nuclei and the $\mu \to e e^{+}e^{-}$ decay, the
strength of the $Z^\prime\mu e$ coupling is estimated and used to calculate the
branching ratio of the $Z^\prime\to \mu e$ decay. This is done for the
so-called $Z_S,\,Z_{LR},\,Z_\chi, Z_\psi$ and $Z_\eta$ bosons. We found that,
through the $\mu-e$ conversion process, the most restrictive bound for the
coupling is provided by the $Z_{LR}$ boson. Meanwhile, by means of the $\mu \to
e e^{+}e^{-}$ decay, the most restrictive bound for the $Z^\prime\mu e$
coupling is provided by the $Z_\chi$ boson. However, if we concentrate on the
less restrictive prediction for the Br($Z^\prime\to \mu e$), this comes from
the $Z_\eta$ boson and the resulting branching ratio is less than $10^{-4}$. On
the other hand, if we consider the most restrictive bound, the branching ratio
for the process is below $2\times 10^{-7}$, which results from the $Z_{RL}$
boson, and is obtained through the $\mu-e$ conversion process.
