A search for new particles (X) that decay to electron or muon pairs has been performed using approximately 200 pb(-1) of p (p) over bar collision data at root s =1.96 TeV collected by the CDF II experiment at the Fermilab Tevatron. Limits on sigma(p (p) over bar -> X)BR(X ->center dot center dot) are presented as a function of dilepton invariant mass m(center dot center dot)>150 GeV/c(2), for different spin hypotheses (0, 1, or 2). The limits are approximately 25 fb for m(center dot center dot)>600 GeV/c(2). Lower mass bounds for X from representative models beyond the standard model including heavy neutral gauge bosons are presented.