The interstellar Nai D absorption-line profiles observed for 15 stars with lines of sight towards the Southern Coalsack are analysed. The method of profile fitting was used in an attempt to determine column densities, linewidths and velocities for the individual interstellar clouds contributing to the observed absorption lines. In common, the observed spectra show a prominent component which is probably associated with the nearest absorbing material composing the Coalsack. The obtained spatial velocity distribution shows great similarity with earlier results from CO emission. In addition, the Nai D data reveal evidence for the existence of two or three other structures with radial velocities of about -22, -33 and -40kms-1. Such components may be the counterparts of interstellar structures observed in diffuse Hα and CO emission. The assumption that at least one of these components originated in the Carina arm imposes ~0.9-1.0kpc as the maximum distance to the near side of that arm.