We present a measurement of the asymmetry ACP between same-sign inclusive dilepton samples ++ and - (=e, μ) from semileptonic B decays in (4S)→BB ̄ events, using the complete data set recorded by the BABAR experiment near the (4S) resonance, corresponding to 471×106 BB ̄ pairs. The asymmetry ACP allows comparison between the mixing probabilities P(B ̄0→B0) and P(B0→B ̄0), and therefore probes CP and T violation. The result, ACP=[-3.9±3.5(stat)±1.9(syst)]×10-3, is consistent with the standard model expectation.