An analysis of the decay B0 -> J/psi K*(892)0 is presented using data, corresponding to an integrated luminosity of 1.0fb^-1, collected in pp collisions at a centre-of-mass energy of 7TeV with the LHCb detector. The polarisation amplitudes and the corresponding phases are measured to be |A_{parallel}|^2 = 0.227 +- 0.004 (stat.) +- 0.011 (syst.), |A_{perp}|^2 = 0.201 +- 0.004 (stat.) +- 0.008 (syst.), delta_{parallel} [rad] = -2.94 +- 0.02 (stat.) +- 0.03 (syst.), delta_{perp} [rad] = 2.94 +- 0.02 (stat.) +- 0.02 (syst.). Comparing B0 -> J/psi K*(892)0 and bar{B}0 -> J/psi bar{K}*(892)0 decays, no evidence for direct CP violation is found.
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