We derive and solve kinetic equations for leptogenesis within the Closed Time Path (CTP) formalism. It is particularly emphasised how the procedure of real intermediate state subtraction familiar from the Boltzmann approach is realised within the CTP framework; and we show how in time-independent situations no lepton asymmetry emerges, in accordance with the CPT theorem. The CTP approach provides new quantum statistical corrections from evaluating the loop integrals. These lead to an enhancement of the asymmetry originating from the Bose statistics of the Higgs particles. To quantify this effect, we define and evaluate an effective CP-violating parameter. We also solve the kinetic equations and show explicitly that the new quantum statistical corrections can be neglected in the strong-washout regime, while, depending on initial conditions, they can be sizable for weak washout.