  We study the lepton flavor violating processes of $\tau^-\to\mu^-PP$ decays
with $PP=K^+K^-,K^0\bar{K}^0,\pi^+\pi^-,\pi^0\pi^0$ in the framework of two
Higgs doublet model III by virtue of the Chiral Perturbation Theory. In this
model, only three neutral Higgs bosons contribute to these decays. With the
current experimental constraints, we show that (a) the contributions of
$|\lambda_{uu(dd)}|$ term are very small for these four decays; (b) we get the
correlation between $|\lambda_{ss}|$ and $|\lambda_{\tau\mu}|$. For
$|\lambda_{\tau\mu}| \sim 10-400$, one has $|\lambda_{ss}|\sim 40-1$; (c) in
the existing model parameter space, $Br(\tau^- \to \mu^- K^+K^-)$ could reach
the order of ${\cal O}(10^{-8})$, but $Br(\tau \to \mu^-
\pi^+\pi^-/\pi^0\pi^0)$ are too small to be observed.
