This Letter reports a search for a narrow resonant state decaying into two W bosons and two b quarks where one W boson decays leptonically and the other decays into a quark-antiquark pair. The search is particularly sensitive to top-antitop resonant production. We use the full data sample of proton-antiproton collisions at a center-of-mass energy of 1.96 TeV collected by the CDF II detector at the Fermilab Tevatron, corresponding to an integrated luminosity of 9.45 fb−1. No evidence for resonant production is found, and upper limits on the production cross section times branching ratio for a narrow resonant state are extracted. Within a specific benchmark model, we exclude a Z′ boson with mass, MZ′, below 915 GeV/c2 decaying into a top-antitop pair at the 95% credibility level assuming a Z′ boson decay width of ΓZ′=0.012MZ′. This is the most sensitive search for a narrow qq¯-initiated tt¯ resonance in the mass region below 750 GeV/c2.