We report on the first direct search for charged Higgs bosons decaying into cs in tt events produced by pp collisions at s√=1.96  TeV. The search uses a data sample corresponding to an integrated luminosity of 2.2  fb−1 collected by the CDF II detector at Fermilab and looks for a resonance in the invariant mass distribution of two jets in the lepton+jets sample of tt candidates. We observe no evidence of charged Higgs bosons in top quark decays. Hence, 95% upper limits on the top quark decay branching ratio are placed at B(t→H+b)< 0.1 to 0.3 for charged Higgs boson masses of 60 to 150  GeV/c2 assuming B(H+→cs¯)=1.0. The upper limits on B(t→H+b) are also used as model-independent limits on the decay branching ratio of top quarks to generic scalar charged bosons beyond the standard model.