We present VLA observations of the absorption spectra of OH (1.667 GHz), H2CO (both 4.83 and 14.5 GHz), and NH3 (23.7 GHz) against the nuclear continuum radio source in Centaurus A. H2CO was also detected against the jet at 4.83 GHz. The nuclear features detected are compared with previous detections of other molecules and neutral hydrogen against the same source. We conclude that the absorption at the systemic velocity of 550 km s-1, attributed to the dark dust lane which crosses the bulge of the galaxy, is produced by either one or more modest-sized molecular clouds or the edge of a large cloud. The same appears to be true in the direction of the jet. A comparison of the new H2CO transitions permits an estimate to be made of the rotational temperature. We obtain a figure of 3.9 K (or lower) which is at the extreme low end of the range for galactic molecular clouds. We have detected a counterpart in OH to the H I features at 576 and 596 km s-1 attributed to gas falling toward the nucleus of Cen A. This feature, centered at about 591 km s-1, is not detected for any other molecule, but there is an extension at the red edge of the H2CO line at 14.5 GHz (and possibly 4.83 GHz) which may also be produced by infaliing gas. There is also weak evidence for 4.83 GHz absorption against the jet at 610 km s-1. Thus, the infalling gas appears to have a distinctive molecular composition and contains fewer molecules than the gas at the systemic velocity. Either the molecular abundances are modified by shock heating in the infall region, or high excitation by the microwave (and other) radiation fields in the nuclear region has reduced the opacity of some molecules.