We report on a search for narrow-width particles decaying to a top and antitop quark pair. The data set used in the analysis corresponds to an integrated luminosity of 680  pb−1 collected with the Collider Detector at Fermilab in run II. We present 95% confidence level upper limits on the cross section times branching ratio. Assuming a specific top-color-assisted technicolor production model, the leptophobic Z′ with width ΓZ′=0.012MZ′, we exclude the mass range MZ′<725  GeV/c2 at the 95% confidence level.