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We study breakdown of $CPT$ symmetry which can occur in the decay process $B\bar B \to l^\pm X^\mp f$ with $f$ being a CP eigenstate. In this process, thestandard model expectations for time ordered semi-leptonic and hadronic events,i.e. which of the two decays takes place first, can be altered in the case thatthere is a violation of the $CPT$ symmetry. To illustrate this possibility, weidentify and study several time integrated observables. We find that anexperiment with $10^{9}$ $B\bar B$ pairs, has the capability for improving thebound on $CPT$ violating parameter or perhaps observe $CPT$ violation.Comment: Revised version to be published in PR

Possible test forCPTinvariance with correlated neutralBdecays