  In this paper we discuss experimental consequences of a novel kind of CPT
violation which would manifest itself in the symmetry of the entangled initial
state of $B ^0$ and $\bar B ^0$ through their loss of indistinguishability. The
``wrong'' symmetry component is proportional to $\omega$. We focus our
theoretical study on the $\Delta t$-dependence of observables concerning
equal-sign dilepton events for which the intensity vanishes at $\Delta t = 0$
in absence of $\omega$. We find that the charge asymmetry, $A_{sl}$, acquires a
$\Delta t$-dependence linear in $\omega$, whose relative importance appears on
specific regions of time still unexplored. We also do a statistical analysis
for the measurements here proposed and find a high sensitivity to this new
CPT-violating effect in this charge asymmetry. We obtain the first limits on
the $\omega$-effect by re-analyzing existing data on the $A_{sl}$ asymmetry.
