Inspired by a significance of $2.4\sigma$ for the $h\to \mu \tau$ decay
observed by the CMS experiment at $\sqrt{s} = 8$ TeV, we investigate the
Higgs lepton-flavor-violating effects in a generic two-Higgs-doublet model
(2HDM), where the lepton-flavor-changing neutral currents are induced at the
tree level and arise from Yukawa sector. To understand the influence of all
involving free parameters and to realize their correlations, we employ
$\chi$-square fitting approach by including theoretical and experimental
constraints. The bounds from Higgs data play the major limits. With
parameter values that simultaneously satisfy the Higgs bounds and the CMS
excess of the Higgs coupling to $\mu$-$\tau$, we find that the tree-level
$\tau\to 3\mu$ and the loop-induced $\tau\to \mu \gamma$ decays are
consistent with current experimental upper limits; the discrepancy in muon
$g-2$ between experimental results and standard model predictions can be
resolved, and an interesting relation between muon $g-2$ and the
branching ratio (BR) for $\mu\to e \gamma$ is found.