A 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 View the MathML sources=8 TeV 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 View the MathML sourcet ̃2 decaying to a lighter top-squark mass eigenstate View the MathML sourcet ̃1 via either View the MathML sourcet ̃2→Ht ̃1 or View the MathML sourcet ̃2→Zt ̃1, followed in both cases by View the MathML sourcet ̃1→tχ ̃10, where View the MathML sourceχ ̃10 is an undetected, stable, lightest supersymmetric particle. The interpretation is performed in the region where the mass difference between the View the MathML sourcet ̃1 and View the MathML sourceχ ̃10 states is approximately equal to the top-quark mass (View the MathML sourcemt ̃1−mχ ̃10≃mt), which is not probed by searches for direct View the MathML sourcet ̃1 squark pair production. The analysis excludes top squarks with masses View the MathML sourcemt ̃2<575 GeV and View the MathML sourcemt ̃1<400 GeV at a 95% confidence level.