Particle Width Effect on $CP$-Violating Asymmetries

$CP$-violating asymmetries calculated from the Breit-Wigner approximation for unstable particle propagators violate $CPT$. A formalism satisfying $CP$ invariance and unitarity is presented. Applications are given to $t$ decays. For the decay $t\to b\nu_{\tau}\bar{\tau}$ in a class of $CP$-violating models the $CP$-violating asymmetry turns out to be $10^{-4}$ times smaller than the previously reported results.