  We study the direct CP violation in the $\tau^\pm\rightarrow K^\pm \rho^0
(\omega)\nu_\tau \rightarrow K^\pm \pi^+\pi^-\nu_\tau$ decay process in the
Standard Model. An interesting mechanism involving the charge symmetry
violating mixing between $\rho^0$ and $\omega$ is applied to enlarge the CP
asymmetry. With this mechanism, the maximum differential and localized
integrated CP asymmetries can reach $-(5.6^{+2.9}_{-1.7})\times10^{-12}$ and
$6.3^{+2.4}_{-3.3}\times 10^{-11}$, respectively, which still leave plenty room
for CP-violating New Physics to be discovered through this process.
