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The $\tau^\pm$, highly polarized in the direction of the incident beam, canbe obtained from the $e^\pm$ collider with the polarized incident $e^-$ (andpreferably also the $e^+$) beam. This polarization vector $\longvecw_i=(w_1+w_2)/(1+w_1w_2) \widehat e_z$ can be used to construct the $T$ oddrotationally invariant product $(\longvec w_i\times\longvec p_\mu)$. $\longvecw_\mu$, where $w_1$ and $w_2$ are longitudinal polarization vectors of $e^-$and $e^+$ respectively; $\longvec p_\mu$ and $\longvec w_\mu$ are the momentumand 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 betested by comparing it with a similar term in $\tau^+$ decay. If T violation insuch a decay is milliweak or stronger, one can find it using the proposedpolarized $\tau$-charm factory with luminosity of $1 \sim 3 \times10^{33}/\cm^2/\sec$. One can test whether T (and CP) violation is due to thecharged Higgs boson exchange by doing a similar experiment for the $\mu^\pm$decay.Comment: 8 pages, uuencoded postscript file. To obtain a copy of this paper  send e-mail to techpub@slac.stanford.ed

Test of T and CP violation in leptonic decay of τ±