Searches for new physics in the tt-bar events at CDF

The authors review the latest results on searches for physics beyond the Standard Model in the top quark sector at CDF Run II in a data sample with integrated luminosity up to 2.8 fb{sup -1}. Since its discovery, the top quark has appeared to be a very special object. It is distinguished by its large mass ({approx} 170 GeV) close to the scale of electroweak symmetry breaking (EWSB), and a Yukawa coupling surprisingly close to one (0.98). Is the top quark mass generated by the Higgs mechanism as the Standard Model (SM) predicts, or does it play a more fundamental role in the EWSB? How would physics beyond the standard model (SM) affect top quark properties? Searches for new physics (NP) should provide answers to the many open questions left by the SM. In these proceedings they present the latest CDF results on the searches for exotic decay modes of the top quark, as well as the production and decay of new particles into final states with a top quark pair. The analyses of the Run II data are performed with approximately 30 times the statistics of the Run I top quark discovery