A search has been performed for Bs0→μ+μ- and B0→μ+μ- decays using 7fb-1 of integrated luminosity collected by the CDF II detector at the Fermilab Tevatron collider. The observed number of B0 candidates is consistent with background-only expectations and yields an upper limit on the branching fraction of B(B0→μ+μ-)<6.0×10-9 at 95% confidence level. We observe an excess of Bs0 candidates. The probability that the background processes alone could produce such an excess or larger is 0.27%. The probability that the combination of background and the expected standard model rate of Bs0→μ+μ- could produce such an excess or larger is 1.9%. These data are used to determine B(Bs0→μ+μ-)=(1.8-0.9+1.1)×10 -8 and provide an upper limit of B(Bs0→μ+μ -)<4.0×10-8 at 95% confidence level. © 2011 American Physical Society.