  We consider CP violating effects in the decays $\tau\rightarrow
(3\pi)\nu_\tau$ where both the ${\rm J}^{\rm P}=1^+$ resonance, $a_1$, and
${\rm J}^{\rm P}=0^-$ resonance, $\pi^\prime$, can contribute. The interference
between the $a_1$ and $\pi^\prime$ resonances can lead to enhanced CP-violating
asymmetries whose magnitudes depend crucially on the $\pi^\prime$ decay
constant, $f_{\pi^\prime}$. We make an estimate of $f_{\pi^\prime}$ with a
simplified chiral Lagrangian coupled to a massive pseudoscalar field, and we
compare the estimates from the non-relativistic quark model and from the QCD
sum rule with the estimate from the `mock' meson model. We then estimate
quantitatively the size of CP-violating effects in a multi-Higgs-doublet model
and scalar-leptoquark models. We find that, while CP-violating effects in the
scalar-leptoquark models may require more than $10^{10}$ $\tau$ leptons,
CP-violating effects from the multi-Higgs-doublet model can be seen at the
$2\sigma$ level with about $10^7$ $\tau$ leptons using the chiral Lagrangian
estimate of $f_{\pi^\prime}=(1\sim 5)\times 10^{-3}$ GeV.
