Lepton Flavor Violating tau --> 3mu Decay in Type-III Two Higgs Doublet Model

We study the current structure of the lepton flavor violating $\tau \to 3\mu$ decay in Type-III 2HDM. This model has many coupling constants which affect this decay. We find that each coupling constant corresponds to the different final-state momenta distribution and vice versa. Using this fact, we suggest how to determine the current structure. We also find the upper limit $\mathrm{\mid }{\eta }_{23}^E{\eta }_{22}^E\mathrm{\mid }<0.00022$ in the case that all Higgs bosons except for the lighter CP even neutral one $h^0$ are decoupled, $M_{h^0}=115$GeV and $\cos \beta =1\mathrm{/}\sqrt{2}$. The observable difference between the MSSM and type-III 2HDM is also discussed.