The dark molecular cloud L134N has been observed at millimeter wavelengths in the CS (J = 3-2), OCS (J = 7-6), and HDO (1(11)-1(10)) transitions. These observations supplement previous observations of L134N detailed in an earlier paper. The CS (J = 3-2) transition was observed at four positions within the cloud, while the other two transitions were observed at one position each. Fractional abundances in the LTE approximation are calculated for each emission line detected. L134N appears to have a high-density core characterized by NH3, C3H2, and (H13CO+)-C-13 emission maps. A lower density envelope characterized by (C18O)-O-18, CS (J = 2-1), and SO emission surrounds the core. In addition, there appears to be a gas phase oxygen abundance gradient in L134N with atomic oxygen depleted in the high-density core. The observed molecular distributions within L134N may be explained by a model in which chemical and physical processes in icy dust grain mantles influence the gas phase molecular abundances.