We report an indirect search for nonstandard model physics using the flavor-changing neutral current decays B→K( *) μ +μ -. We reconstruct the decays and measure their angular distributions, as a function of q2=Mμμ2c2, where M μμ is the dimuon mass, in pp̄ collisions at √s=1.96TeV using a data sample corresponding to an integrated luminosity of 6.8fb -1. The transverse polarization asymmetry AT(2) and the time-reversal-odd charge-and-parity asymmetry A im are measured for the first time, together with the K * longitudinal polarization fraction F L and the muon forward-backward asymmetry A FB for the decays B0→K *0μ +μ - and B +→K *+μ +μ -. The B→K *μ +μ - forward-backward asymmetry in the most sensitive kinematic regime, 1≤q2<6GeV2/c2, is measured to be A FB=0.29-0.23+0.20(stat) ±0.07(syst), the most precise result to date. No deviations from the standard model predictions are observed. © 2012 American Physical Society.