We present a label-free single-molecule based sensing platform using a carbon nanotube field-effect transistor. By point functionalizing a carbon nanotube through an electrochemical oxidation reaction, the conductance becomes sensitive and chemically reactive at a single point to which we can covalently attach a probe DNA molecule. Two-level fluctuations appear in the conductance of the carbon nanotube when it is immersed in a liquid buffer solution containing complementary target DNA. We show that the autocorrelation of the conductance can be used to extract DNA hybridization kinetics. The results are comparable to the one extracted through a hidden Markov model.