Mn 3d electronic states in the dilute magnetic semiconductor Zn_1−xMn_xS (x=0.1-0.3) are studied using X-ray emission (XES) measurements and density functional theory (DFT). Mn L_2,3 emission spectra of Zn_1−xMn_xS (x=0.1-0.3) suggest that the Mn impurities do not form clusters in the host ZnS lattice, in agreement with previous models. A shift in the position of a MnL₃ XES feature suggests a change in the nature of the hybridization between the Mn 3d_3/2 and S 3p states as a function of x. Our DFT calculations reproduce the weak interatomic exchange interaction, as well as the strong intra-atomic exchange splitting that is expected from observations of Zeeman splitting in such materials.