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 collisions at 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 σBR(pp→X→μμ), 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.