We use 106 pb (-1) of data collected with the Collider Detector at Fermilab to search for narrow-width, vector particles decaying to a top and an antitop quark. Model independent upper limits on the cross section for narrow, vector resonances decaying to t&tmacr; are presented. At the 95% confidence level, we exclude the existence of a leptophobic Z' boson in a model of top-color-assisted technicolor with mass M(Z')<480 GeV/c(2) for natural width gamma = 0.012M(Z'), and M(Z')<780 GeV/c(2) for gamma = 0.04M(Z').