We consider CP violating effects in the decays τ → (3π)ν τ where both the J P = 1 + resonance, a 1 , and J P = 0 − resonance, π ′ , can contribute. The interference between the a 1 and π ′ resonances can lead to enhanced CP-violating asymmetries whose magnitudes depend crucially on the π ′ decay constant,We make an estimate of f π ′ with a simplified chiral Lagrangian coupled to a massive pseudoscalar field, and we compare the estimates from the nonrelativistic quark model and from the QCD sum rule with the estimate from the 'mock' meson model. We then estimate quantitatively the size of CPviolating 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 τ leptons, CP-violating effects from the multi-Higgsdoublet model can be seen at the 2σ level with about 10 7 τ leptons using the chiral Lagrangian estimate of f π ′ = (1 ∼ 5) × 10 −3 GeV.