  Recent data from the ATLAS and CMS detectors at the Large Hadron Collider at
CERN give a hint of possible violation of flavor in the leptonic decays of the
Higgs boson. In this work we analyze the flavor violating leptonic decays
$H^0_1\to l_i \bar l_j$ ($i\neq j$) within the framework of an MSSM extension
with a vectorlike leptonic generation. Specifically we focus on the decay mode
$H^0_1\to \mu\tau$. The analysis is done including tree and loop contributions
involving exchange of $W, Z$, charge and neutral higgs and leptons and mirror
leptons, charginos and neutralinos and sleptons and mirror sleptons. It is
found that a substantial branching ratio of $H^0_1\to \mu\tau$, i.e., of as
much a ${\cal{O}}(1)\%$, can be achieved in this model, the size hinted by the
ATLAS and CMS data. The flavor violating decays $H^0_1\to e\mu, e\tau$ are also
analyzed and found to be consistent with the current experimental limits. An
analysis of the dependence of flavor violating decays on CP phases is given.
The analysis is extended to include flavor decays of the heavier Higgs bosons.
A confirmation of the flavor violation in Higgs boson decays with more data
that is expected from LHC at $\sqrt s=13$ TeV will be evidence of new physics
beyond the standard model.
