An analysis of the decay B0→J/ψK∗(892)0 is presented using data, corresponding to an integrated luminosity of 1.0  fb−1, collected in pp collisions at a center-of-mass energy of 7 TeV with the LHCb detector. The polarization amplitudes and the corresponding phases are measured to be |A∥|2=0.227±0.004 (stat)±0.011 (syst), |A⊥|2=0.201±0.004 (stat)±0.008 (syst), δ∥[rad]=−2.94±0.02 (stat)±0.03 (syst), and δ⊥[rad]=2.94±0.02 (stat)±0.02 (syst). Comparing B0→J/ψK∗(892)0 and ¯¯¯B0→J/ψ¯¯¯¯K∗(892)0 decays, no evidence for direct CP violation is found.