A search has been performed for B{sub s}{sup 0} {yields} {mu}{sup +}{mu}{sup -} and B{sup 0} {yields} {mu}{sup +}{mu}{sup -} decays using 7 fb{sup -1} of integrated luminosity collected by the CDF II detector at the Fermilab Tevatron collider. The observed number of B{sup 0} candidates is consistent with background-only expectations and yields an upper limit on the branching fraction of {Beta}(B{sup 0} {yields} {mu}{sup +}{mu}{sup -}) < 6.0 x 10{sup -9} at 95% confidence level. We observe an excess of B{sub s}{sup 0} 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 B{sub s}{sup 0} {yields} {mu}{sup +}{mu}{sup -} could produce such an excess or larger is 1.9%. These data are used to determine {Beta}(B{sub s}{sup 0} {yields} {mu}{sup +}{mu}{sup -}) = (1.8{sub -0.9}{sup +1.1}) x 10{sup -8} and provide an upper limit of {Beta}(B{sub s}{sup 0} {yields} {mu}{sup +}{mu}{sup -}) < 4.0 x 10{sup -8} at 95% confidence level