Our search for supersymmetry through the direct pair production of top squarks, with Higgs (H) or Z bosons in the decay chain, is performed using a data sample of proton–proton collisions at √s= 8TeV collected in 2012 with the CMS detector at the LHC. The sample corresponds to an integrated luminosity of 19.5 fb-1. The search is performed using a selection of events containing leptons and bottom-quark jets. No evidence for a significant excess of events over the standard model background prediction is observed. The results are interpreted in the context of simplified supersymmetric models with pair production of a heavier top-squark mass eigenstate t̃/sup2 source decaying to a lighter top-squark mass eigenstate t̃/sup2 via either t̃/sup2 → Ht̃/sup1 or tsup̃/sup2 →Ztsup̃/sup1, followed in both cases by tsup̃/sup1→ t?sup0̃1, where ?sup0̃1 source is an undetected, stable, lightest supersymmetric particle. The interpretation is performed in the region where the mass difference between the tsup̃/sup1 and ?sup0̃1 states is approximately equal to the top-quark mass (mt1-msup?01≃mt), which is not probed by searches for direct tsup̃/sup1 squark pair production. This analysis excludes top squarks with mass mt1 575 GeVand msubt2