TEST OF T AND CP VIOLATION IN LEPTONIC DECAY OF tau^+-

The $\tau^\pm$, highly polarized in the direction of the incident beam, can be obtained from the $e^\pm$ collider with the polarized incident $e^-$ (and preferably also the $e^+$) beam. This polarization vector $\longvec w_i=(w_1+w_2)/(1+w_1w_2) \widehat e_z$ can be used to construct the $T$ odd rotationally invariant product $(\longvec w_i\times\longvec p_\mu)$. $\longvec w_\mu$, where $w_1$ and $w_2$ are longitudinal polarization vectors of $e^-$ and $e^+$ respectively; $\longvec p_\mu$ and $\longvec w_\mu$ are the momentum and polarization of the muon in the decay $\tau^-\rarrow \mu^-+ \bar\nu_\mu+\nu_\tau$. T is violated by the existence of such a term. CP can be tested by comparing it with a similar term in $\tau^+$ decay. If T violation in such a decay is milliweak or stronger, one can find it using the proposed polarized $\tau$-charm factory with luminosity of $1 \sim 3 \times 10^{33}/\cm^2/\sec$. One can test whether T (and CP) violation is due to the charged Higgs boson exchange by doing a similar experiment for the $\mu^\pm$ decay.