CP Violation and the Width $Z\rightarrow b\bar{b}$

We discuss the effect of CP-violating $Zb\bar{b}$, $Zb\bar{b}G$ and $Zb\bar{b}\gamma$ couplings on the width $\Gamma(Z\rightarrow b\bar bX)$. The presence of such couplings leads in a natural way to an increase of this width relative to the prediction of the standard model. Various strategies of a direct search for such CP-violating couplings by using CP-odd observables are outlined. The number of $Z$ bosons required to obtain significant information on the couplings in this way is well within the reach of present LEP experiments.