We report the results of a search for T and CP violation in B0-B̅ 0 mixing using an inclusive dilepton sample collected by the BABAR experiment at the PEP-II B Factory. The asymmetry between ℓ+ℓ+ and ℓ-ℓ- events allows us to compare the probabilities for B̅ 0→B0 and B0→B̅ 0 oscillations and thus probe T and CP invariance. Using a sample of 23×106 BB̅ pairs, we measure a same-sign dilepton asymmetry of AT/CP = [0.5±1.2(stat)±1.4(syst)]%. For the modulus of the ratio of complex mixing parameters p and q, we obtain |q/p| = 0.998±0.006(stat)±0.007(syst).
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