  The issue of testing CPT invariance at a $B$ factory is considered. We
present asymmetries that permit a clean extraction of quantities parametrizing
direct and indirect CPT violation, using information from $\Upsilon(4S)$ decay
via coherent $B_d\overline{B_d}$ pairs into various final states. Estimates are
given of the bounds on CPT violation that could be obtained in present and
planned machines.
