We have performed three-dimensional, non-LTE (non-local thermodynamic equilibrium) radiative transfer calculations for ¹²CO and ¹³CO lines, applying them to our high-resolution hydrodynamic models of the torus around a supermassive black hole in an active galactic nucleus. The hydrodynamic simulations reveal inhomogeneous and turbulent gas structure on a subparsec scale in a circumnuclear starburst region. Thick disks interlaced with filaments, clumps, and holes are naturally formed as a result of the interplay among energy feedback from supernovae, self-gravity of the gas, galactic rotation, and radiative cooling. The intensity maps of the molecular lines for the circumnuclear disks show a clumpy structure, reflecting the intrinsic inhomogeneity and turbulent motion of the gas disk. The fine structure of the torus could be resolved in nearby active galaxies using the Atacama Large Millimeter Array. We also found that the CO-to-H₂ conversion factor (X-factor) is not uniformly distributed in the central 100 pc region. The X-factor derived for ¹²CO (J = 1 - 0) intensity depends strongly on the intensity, whereas the X for ¹²CO (J = 3 - 2) is nearly constant over 2 orders of magnitude of the intensity. The suggested conversion factor for the molecular gas mass is XCO(J=3 - 2) ~ 0.27 x 10²⁰ cm^-2 (K km s^-1)^-1. The line ratio of high-J transitions of CO is not uniformly distributed in the nuclear disk, and the apparent ratio depends on the beam sizes. Observed ¹²CO(J = 4 - 3)/¹²CO(J = 2 - 1) can differ from the intrinsic ratio by as much as 20%.