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A key issue in heavy fermion research is how subtle changes in the hybridization between the 4f (5f) and conduction electrons can result in fundamentally different ground states. CeRhIn₅ stands out as a particularly notable example-- replacing Rh by either Co or Ir, located above or below Rh in the periodic table, antiferromagnetism gives way to superconductivity. In this photoemission study of CeRhIn₅, we demonstrate that the use of resonant ARPES with polarized light allows to extract detailed information on the 4f crystal field states together with details on the 4f and conduction electrons hybridization which together determine the ground state. We directly observe weakly dispersive Kondo resonances of f-electrons and identify two of the three Ce 4f¹_5/2 crystal-electric-field levels. In particular, we observe band-dependent hybridization, which directly relates to the fact that the hybridization occurs primarily between the Ce 4f states in the CeIn₃ layer and two more three-dimensional bands composed of the Rh 4d and In 5p orbitals in the RhIn₂ layer. Our results allow to connect the properties observed at elevated temperatures with the unusual low-temperature properties of this enigmatic heavy fermion compound.