I describe the generation of the observed matter-antimatter asymmetry in the Universe through Leptogenesis at early epochs, due to spontaneous violation of CPT symmetry in string-inspired models. The latter is induced by appropriate (temperature-dependent, in general) backgrounds of the antisymmetric tensor (Kalb-Ramond (KR)) field that appears in the (bosonic) massless multiplet of strings. In four space-time dimensions, the KR field is known to be dual to a (massless) pseudoscalar field (KR axion), which plays a crucial role in generating the lepton asymmetry at early times in models involving heavy right-handed neutrinos which decay (at tree level) to leptons in the standard model sector of the (low-energy) effective theory, in the presence of the CPT-Violating background of the KR axion. This lepton asymmetry is then communicated to the baryon sector by Baryon-minus-Lepton-number conserving processes. The model respects the stringent current bounds on CPT Violation, albeit requires a fine tuning of the vacuum energy. As a byproduct of the analysis, I also discuss the potential role of quantum fluctuations of the KR axion on the (anomalous) radiative generation of a Majorana mass for the right-handed neutrinos themselves.