We report results of a search for the pair production of the lightest supersymmetric partner of the top quark using 1 fb-1 of data collected by the D0 detector at a ppbar center-of-mass energy of 1.96 TeV at the Fermilab Tevatron Collider. Both scalar top quarks are assumed to decay into a b quark, a charged lepton and a scalar neutrino. The search is performed in the electron plus muon and dielectron final states. The signal topology consists of two isolated leptons, missing transverse energy, and jets. We find no evidence for this process and exclude regions of parameter space in the framework of the minimal supersymmetric standard model.