This paper reports a search for nonstandard model topquark resonances, Z', decaying to t (t) over bar -> W(+)bW(-)(b) over bar, 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 p (p) over bar 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 Gamma(Z') = 0.012M(Z'). Within this model, we exclude a Z' boson with masses below 805 GeV/c(2) at the 95% confidence level. RI 钟, 伟/G-9952-2011; De Cecco, Sandro/B-1016-2012; Robson, Aidan/G-1087-2011; Prokoshin, Fedor/E-2795-2012