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 $hto e_4^pm mu^mp$,
where $e_4$ is the new lepton, can be significant when this process is kinematically allowed. Subsequent decays $e_4^pm to Zmu^pm$ and $e_4^pm to W^pm u$ lead to the same final states as $h to ZZ^* to Z mu^+mu^-$ and $h to WW^* to W mu u$, thus possibly affecting measurements of these processes. We calculate $hto e_4 ell_i to Zell_iell_j$, where $ell_{i,j}$ are standard model leptons, including the possibility of off-shell decays, interference with $hto ZZ^* to Z ell_i ell_i$, 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 $hto 4ell$. We focus on the couplings of the muon and discuss possible effects on $hto ZZ^*$ from the region of parameters that can explain the anomaly in the measurement of the muon g-2.
