We present a measurement of the asymmetry A C P between same-sign inclusive dilepton samples ℓ + ℓ + and ℓ − ℓ − ( ℓ = e , μ ) from semileptonic B decays in Υ ( 4 S ) → B ¯ B events, using the complete data set recorded by the BABAR experiment near the Υ ( 4 S ) resonance, corresponding to 471 × 1 0 6 B ¯ B pairs. The asymmetry A C P allows comparison between the mixing probabilities P ( ¯ B 0 → B 0 ) and P ( B 0 → ¯ B 0 ) , and therefore probes C P and T violation. The result, A C P = [ − 3.9 ± 3.5 ( stat ) ± 1.9 ( syst ) ] × 1 0 − 3 , is consistent with the standard model expectation.