The crystal-field splittings and the spectral properties of the CeM₂Si₂ compounds (M=Ru, Rh, and Pd) are studied by means of an ab initio many-body combined technique. The hybridization function is obtained using the local-density approximation and the full-potential linear augmented plane wave method and is used as input to the Anderson impurity model. The Kondo physics is obtained by solving this model within an extended noncrossing approximation. The calculated crystal electric-field (CEF) splittings are compared with the contradictory experimental data and helped in the correct assignment of their symmetries. In particular, it is shown that the CeRh₂Si₂ has the largest CEF splittings and the highest Kondo temperature, in good agreement with experimental data. The position of the bare energy f level is found to affect slightly the CEF splittings but does not change their symmetries.