As a probe of the AGN feeding and feedback, we trace the distribution and kinematics of the warm molecular gas (H2 2.12 microns) and ionized gas (BrG 2.16 microns) in the Keck OSIRIS Nearby AGN (KONA) survey of 40 local, representative AGN. The warm molecular gas is found to be distributed throughout the central 500 pc region in comparison to the ionized gas, which has a significantly more centrally concentrated surface brightness profile. Taking the circumnuclear disk geometry into account, the half-width-half-maximum of the molecular hydrogen flux distribution is typically 35-40 pc compared to 25 pc for the BrG flux emission. One interpretation considered to explain this distribution difference of ionized versus molecular gas is excitation where the ionized gas is excited by AGN radiation closer to the AGN, while excitation of the molecular gas is dominated by thermal processes extending beyond the immediate vicinity of the AGN. The total ionized gas mass within r < 100 pc ranges from (7-30) x 105 Msun, with surface mass densities of 1-100 Msun/pc2. Within this same region the total molecular gas is found to be 103-5 times lower, with surface mass densities of 0.7-12 x 10-3 Msun/pc2. This suggests an available gas reservoir within the central 200 pc that exceeds that needed to feed the AGN by at least one, and up to three, orders of magnitude.