  We study the LFV Higgs production processes
$e^-\gamma\to\ell^-\phi\;(\ell=\mu,\tau; \phi=H, A)$ as a probe of Higgs
mediated LFV couplings at an electron-photon collider, where $H$ and $A$ are
extra CP even and odd Higgs bosons, respectively, in the two Higgs doublet
model. Under the constraints from the current data of muon and tau rare decay,
the cross section can be significantly large. It would improve the experimental
upper bounds on the effective LFV coupling constants. In addition, the
chirality nature of the LFV Higgs coupling constants can be measured by
selecting electron beam polarizations.
