  The mixing of new vectorlike leptons with leptons in the standard model can
generate flavor violating couplings of $h$, $W$ and $Z$ between heavy and light
leptons. Focusing on the couplings of the muon, the partial decay width of
$h\to e_4^\pm \mu^\mp$, where $e_4$ is the new lepton, can be significant when
this process is kinematically allowed. Subsequent decays $e_4^\pm \to Z\mu^\pm$
and $e_4^\pm \to W^\pm \nu$ lead to the same final states as $h \to ZZ^* \to Z
\mu^+\mu^-$ and $h \to WW^* \to W \mu\nu$, thus possibly affecting measurements
of these processes. We calculate $h\to e_4 \ell_i
  \to Z\ell_i\ell_j$, where $\ell_{i,j}$ are standard model leptons, including
the possibility of off-shell decays, interference with $h\to ZZ^* \to Z \ell_i
\ell_i$, and the mass effect of $\ell_{i,j}$ which are important when the mass
of $e_4$ is close to the mass of the Higgs boson. We derive constraints on
masses and couplings of the heavy lepton from the measurement of $h\to 4\ell$.
We focus on the couplings of the muon and discuss possible effects on $h\to
ZZ^*$ from the region of parameters that can explain the anomaly in the
measurement of the muon g-2.
