  We report on a search for \bsmm\ and \bdmm\ decays using proton-antiproton
collision data at $\sqrt{s}=1.96$ TeV corresponding to $10 \fb$ of integrated
luminosity collected by the CDF detector at the Fermilab Tevatron collider. The
observed number of \bd\ candidates is consistent with background-only
expectations and yields an upper limit on the branching fraction of $\brbdmm <
4.6\times 10^{-9}$ at 95% confidence level. We observe an excess of \bs\
candidates. The probability that the background processes alone could produce
such an excess or larger is 0.94%. The probability that the combination of
background and the expected standard model rate of \bsmm\ could produce such an
excess or larger is 6.8%. These data are used to determine a branching fraction
$\brbsmm = (1.3^{+0.9}_{-0.7}) \times 10^{-8} $ and provide an upper limit of
$\brbsmm < 3.1\times 10^{-8}$ at 95% confidence level.
