This paper reports a search for nonstandard model topquark resonances, Z′, decaying to tt→W+bW−b, where both W decay to quarks. We examine the top-antitop quark invariant mass spectrum for the presence of narrow resonant states. The search uses a data sample of pp collisions at a center of mass energy of 1.96 TeV collected by the CDF II detector at the Fermilab Tevatron, with an integrated luminosity of 2.8  fb−1. No evidence for top-antitop quark resonant production is found. We place upper limits on the production cross section times branching ratio for a specific topcolor assisted technicolor model in which the Z′ has a width of ΓZ′=0.012MZ′. Within this model, we exclude a Z′ boson with masses below 805  GeV/c2 at the 95% confidence level.