We have mapped the central region of NGC 4945 in the $J=2to1$ transition of $^{12}$CO, $^{13}$CO, and C$^{18}$O, as well as the continuum at 1.3 mm, at an angular resolution of $5farc times 3farc$ with the Submillimeter Array. The relative proximity of NGC 4945 (distance of only 3.8 Mpc) permits a detailed study of the circumnuclear molecular gas and dust in a galaxy exhibiting both an AGN (classified as a Seyfert 2) and a circumnuclear starburst in an inclined ring with radius $sim$2farcs5 ($sim$50 pc). We find that all three molecular lines trace an inclined rotating disk with major axis aligned with that of the starburst ring and large-scale galactic disk, and which exhibits solid-body rotation within a radius of $sim$5farc ($sim$95 pc). We infer an inclination for the nuclear disk of $62^{circ} pm 2^{circ}$, somewhat smaller than the inclination of the large-scale galactic disk of $sim$$78^{circ}$. The continuum emission at 1.3 mm also extends beyond the starburst ring, and is dominated by thermal emission from dust. If it traces the same dust emitting in the far-infrared, then the bulk of this dust must be heated by star-formation activity rather than the AGN. We discover a kinematically-decoupled component at the center of the disk with a radius smaller than $1farcs4$ (27 pc), but which spans approximately the same range of velocities as the surrounding disk. This component has a higher density than its surroundings, and is a promising candidate for the circumnuclear molecular torus invoked by AGN unification models.
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