  An angular analysis of the decay $B^0 \to \phi K^*(892)^0$ is reported based
on a $pp$ collision data sample, corresponding to an integrated luminosity of
1.0 fb$^{-1}$, collected at a centre-of-mass energy of $\sqrt{s} = 7$ TeV with
the LHCb detector. The P-wave amplitudes and phases are measured with a greater
precision than by previous experiments, and confirm about equal amounts of
longitudinal and transverse polarization. The S-wave $K^+ \pi^-$ and $K^+K^-$
contributions are taken into account and found to be significant. A comparison
of the $B^0 \to \phi K^*(892)^0$ and $\bar{B}^0 \to \phi \bar{K}^*(892)^0$
results shows no evidence for direct CP violation in the rate asymmetry, in the
triple-product asymmetries or in the polarization amplitudes and phases.
