We present ~2'' resolution CO (3-2), HCO+(4-3), and 880 μm continuum images of the luminous infrared galaxy NGC 6240 obtained at the Submillimeter Array. We find that the spatially resolved CO (3-2), HCO + (4-3), and the 880 μm emission peaks between the two nuclear components that are both known to harbor AGNs. Our large velocity gradient (LVG) analysis performed on each velocity channel suggests that the peak of the molecular gas emission traced in our observations is warm (T = 20-100 K), dense (nH2 = 105.0-105.4 cm-3), and moderately optically thin (τ = 0.2-2) in the central 1 kpc. We also find large column densities of ~1023 cm-2. Such extreme conditions are observed over ~300 km s-1 centered around the CO-derived systemic velocity. The derived molecular gas mass from the CO (3-2) emission and a CO-to-H2 conversion factor commonly used for ULIRGs is (6.9 ± 1.7) × 109 M, and this is consistent with the mass derived from previous CO (2-1) observations. The gas is highly turbulent in the central kpc (ΔvFWZI ~ 1175 km s-1). Furthermore, possible inflow or outflow activity is suggested from the CO (3-2) velocity distribution. We tentatively state that 3.5 × 108 M of isolated CO (3-2) emission seen west of the northern disk may be associated with outflows from starburst superwinds, but the gas outflow scenario from one of the central AGN is not completely ruled out. Piecing all of the information together, the central region of NGC 6240 harbors 2 AGNs, ~1010 M of molecular gas mass, 5 × 107 M of dust mass, and has possible evidence of inflow and outflow activity.