Lepton Flavor Violation in the Higgs Boson Decay at a Linear Collider

We study possibility of observing the process $h^{0} \to \tau^{\pm} \mu^{\mp}$ at a linear collider. The branching ratio is constrained to be of the order of $10^{-4}$ by the $\tau^{-} \to \mu^{-} \eta$ result. Supersymmetric standard models can reproduce such amount of the branching ratio by taking a specific parameter set. The Higgsstrahlung process $e^{+}e^{-} \to Zh^{0}$ is preferable because of its simple kinematic structure, then, the signal process is $e^{+} e^{-} \to Z h^{0} \to Z \tau^{\pm} \mu^{\mp}$. The most serious background comes from the process, $e^{+} e^{-} \to Zh^{0} \to Z\tau^{\pm} \tau^{\mp} \to \tau^{\pm} \mu^{\mp} \nu \bar{\nu}$. We estimate the significance of the signal, taking into account the background reduction.