We present a search for high-mass neutral resonances using dimuon data corresponding to an integrated luminosity of 2.3 fb[superscript -1] collected in pp̅ 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(pp̅ →X→μμ̅ ), 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. Academy of Finland Slovak R&D Agency Programa Consolider-Ingenio 2010, Spain Ministerio de Ciencia e Innovación, Spain Russian Foundation for Basic Research Institut National de Physique Nucleaire et Physique des Particules/CNRS Royal Society, United Kingdom Science and Technology Facilities Council, United Kingdom Korean Research Foundation Korean Science and Engineering Foundation Bundesministerium für Bildung und Forschung, Germany Alfred P. Sloan Foundation Swiss National Science Foundation National Science Council of the Republic of China Natural Sciences and Engineering Research Council of Canada Ministry of Education, Culture, Sports, Science and Technology of Japan Italian Istituto Nazionale di Fisica Nucleare National Science Foundation United States Department of Energy