We present a search for high-mass neutral resonances using dimuon data corresponding to an integrated luminosity of 2.3 fb(-1) collected in pp[over ] collisions at sqrt[s]=1.96 TeV by the CDF II detector at the Fermilab Tevatron. No significant excess above the standard model expectation is observed in the dimuon invariant-mass spectrum. We set 95% confidence level upper limits on sigmaBR(pp-->X-->micromicro), where X is a boson with spin-0, 1, or 2. Using these cross section limits, we determine lower mass limits on sneutrinos in R-parity-violating supersymmetric models, Z' bosons, and Kaluza-Klein gravitons in the Randall-Sundrum model.