High-resolution observations of edge-on protoplanetary disks in emission from molecular species that sample different critical densities and formation pathways offer the opportunity to trace the vertical chemical and physical structures of protoplanetary disks. Among the problems that can be addressed is the origin and significance of the bright CN emission that is a ubiquitous feature of disks. Based on analysis of subarcsecond-resolution Atacama Large Millimeter Array archival data for the edge-on Flying Saucer disk (2MASS J16281370-2431391), we establish the vertical and radial differentiation of the CN emitting regions of the disk with respect to those of 12CO and CS, and we model the physical disk conditions from which the CN emission arises. We demonstrate that the 12CO (2–1), CN (2–1), and CS J = 5–4 emitting regions of the disk decrease in scale height above the midplane, such that 12CO, CN, and CS trace layers of increasing density and decreasing temperature. We find that at radii >100 au from the central star, CN emission predominantly arises from intermediate layers, while in the inner region of the disk CN appears to arise from layers closer to the midplane. We investigate the physical conditions of the disk within the CN emitting regions, as well as the ranges of CN excitation temperature and column density, via RADEX non-local thermodynamic equilibrium (non-LTE) modeling of the three brightest CN hyperfine lines. Near the disk midplane, where we derive densities of nH2 ~ 107 cm−3 at relatively low Tkin (~12 K), we find that CN is thermalized, while sub-thermal, non-LTE conditions appear to obtain CN emission from higher (intermediate) disk layers. We consider whether and how the particular spatial location and excitation conditions of CN emission from the Flying Saucer can be related to CN production that is governed, radially and vertically, by the degree of irradiation of the flared disk by X-rays and UV photons from the central star.