We report on a combined experimental and theoretical study on CrI3 single crystals by employing the polarization dependence of resonant inelastic x-ray scattering (RIXS). Our investigations reveal multiple Cr 3d orbital splitting (dd excitations) as well as magnetic dichroism (MD) in the RIXS spectra. The dd excitation energies are similar on the two sides of the ferromagnetic transition temperature, T-C similar to 61 K, although MD in RIXS is predominant at 0.4 T magnetic field below TC. This demonstrates that the ferromagnetic superexchange interaction that is responsible for the interatomic exchange field is vanishingly small compared with the local exchange field that comes from exchange and correlation interaction among the interacting Cr 3d orbitals. The recorded RIXS spectra reported here reveal clearly resolved Cr 3d intraorbital dd excitations that represent transitions between electronic levels that are heavily influenced by dynamic correlations and multiconfiguration effects. Our calculations taking into account the Cr 3d hybridization with the ligand valence states and the full multiplet structure due to intra-atomic and crystal field interactions in Oh and D3d symmetry clearly reproduced the dichroic trend in experimental RIXS spectra.