In this study, we investigate the line emissions from cold molecular gas based on our previous "radiation-driven fountain model" (Wada et al. 2016), which reliably explains the spectral energy distribution of the nearest type 2 Seyfert galaxy, the Circinus galaxy. Using a snapshot of the best-fit radiation-hydrodynamic model for the central r ≤ 16 pc, in which non-equilibrium X-ray-dominated region chemistry is solved, we conduct post-processed, non-local thermodynamic equilibrium radiation transfer simulations for the CO lines. We obtain a spectral line energy distribution with a peak around J 6, and its distribution suggests that the lines are not thermalized. However, for a given line-ofsight, the optical depth distribution is highly non-uniform between τ ν 1 and τ ν 1. The CO-to-H 2 conversion factor (X CO ), which can be directly obtained from the results, is not a constant and depends strongly on the integrated intensity, and it differs from the fiducial value for local objects. X CO exhibits a large dispersion of more than one order of magnitude, reflecting the non-uniform internal structure of a "torus." We also found that the physical conditions differ between grid cells on a scale of a few parsecs along the observed lines of sight; therefore, a specific observed line ratio does not necessarily represent a single physical state of the ISM.