The angular distributions and the differential branching fraction of the decay $B^0 \to K^*(892)^0 \mu^+ \mu^-$ are studied using a data sample corresponding to an integrated luminosity of 5.2 inverse femtobarns collected with the CMS detector at the LHC in pp collisions at $\sqrt{s}$ = 7 TeV. From more than 400 signal decays, the forward-backward asymmetry of the muons, the $K^*(892)^0$ longitudinal polarization fraction, and the differential branching fraction are determined as a function of the square of the dimuon invariant mass. The measurements are in good agreement with standard model predictions