We report on a search for Bs0겏꺤+꺤- and B0겏꺤+꺤- decays using proton-antiproton collision data at 곥s=1.96 TeV corresponding to 10 fb-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