We present high resolution images of the 12CO(2-1) emission in the central 1' (1 kpc) of NGC 5128 (Centaurus A), observed using the SMA. We elucidate for the first time the distribution and kinematics of the molecular gas in this region with a resolution of 6'.0 x 2'.4 (100 pc x 40 pc). We spatially resolve the circumnuclear molecular gas in the inner 24'' x 12'' (400 pc x 200 pc), which is elongated along a position angle P.A. = 155 deg and perpendicular to the radio/X-ray jet. The SE and NW components of the circumnuclear gas are connected to molecular gas found at larger radii. This gas appears as two parallel filaments at P.A. = 120 deg, which are coextensive with the long sides of the 3 kiloparsec parallelogram shape of the previously observed dust continuum, as well as ionized and pure rotational H2 lines. Spatial and kinematical asymmetries are apparent in both the circumnuclear and outer gas, suggesting non-coplanar and/or non-circular motions. We extend to inner radii (r < 200 pc) previously studied warped disk models built to reproduce the central parallelogram-shaped structure. Adopting the warped disk model we would confirm a gap in emission between the radii r = 200 - 800 pc (12'' - 50''), as has been suggested previously. Although this model explains this prominent feature, however, our 12CO(2-1) observations show relevant deviations from this model. Namely, the physical connection between the circumnuclear gas and that at larger radii, brighter SE and NW sides on the parallelogram-shaped feature, and an outer curvature of its long sides. Overall it resembles more closely an S-shaped morphology, a trend that is also found in other molecular species. Hence, we explore qualitatively the possible contribution of a weak bi-symmetric potential which would naturally explain these peculiarities.