We present a measurement of the asymmetry A_{CP} between same-sign inclusive dilepton samples ℓ^{+}ℓ^{+} and ℓ^{-}ℓ^{-} (ℓ=e, μ) from semileptonic B decays in ϒ(4S)→BB[over ¯] events, using the complete data set recorded by the BABAR experiment near the ϒ(4S) resonance, corresponding to 471×10^{6} BB[over ¯] pairs. The asymmetry A_{CP} allows comparison between the mixing probabilities P(B[over ¯]^{0}→B^{0}) and P(B^{0}→B[over ¯]^{0}), and therefore probes CP and T violation. The result, A_{CP}=[-3.9±3.5(stat)±1.9(syst)]×10^{-3}, is consistent with the standard model expectation.