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 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 decaying to a lighter top-squark mass eigenstate via either or , followed in both cases by , where is an undetected, stable, lightest supersymmetric particle. The interpretation is performed in the region where the mass difference between the and states is approximately equal to the top-quark mass (), which is not probed by searches for direct squark pair production. The analysis excludes top squarks with masses and at a 95% confidence level.