We have observed the J = 3 --> 2 and J = 2 --> 1 lines of (CO)-C-13 and (CO)-C-13 with 22"-24" resolution in the central region of the spiral galaxy NGC 253. The (CO)-C-13 J = 3 --> 2 emission is pointlike (less-than-or-similar-to 15"), whereas the emission in the other CO lines is consistent with emission from a approximately 40" x 10" FWHM bar. The ratio of (CO)-C-13 J = 3 --> 2 to (CO)-C-13 J = 2 --> 1 line intensities toward the nucleus requires warm (T(K) greater-than-or-similar-to 100 K), dense [n(H2) greater-than-or-similar-to 10(4)-10(5) cm-3] molecular gas. Spatial coincidence of 3 mm continuum and [Ne II] 12.8-mu-m emission from H II regions and mid-IR emission from hot dust with the (CO)-C-13 J = 3 --> 2 emission implies a common source of excitation, possibly related to the intense star formation that has occurred in the nucleus. The decline in the (CO)-C-13 J = 3 --> 2 intensity with distance from the nucleus reflects a decline in both density and temperature. The declining density, for the bulk of the CO line-emitting gas, is inferred from the drop in the (CO)-C-13 J = 3 --> 2/(CO)-C-13 J = 2 --> 1 intensity ratio, while the small (CO)-C-13 J = 3 --> 2 source size compared to the size of the emission region for lines of high dipole moment molecules (e.g., CS J = 2 --> 1) implies a decline in gas temperature. A drop in the (CO)-C-13 J = 3 --> 2/J = 2 --> 1 intensity ratio indicates that the molecular gas density is low 30" from the nucleus. The molecular gas mass in the central 50", estimated from the optically thin lines of (CO)-C-13, is approximately 4 x 10(7) M..