In this work, we performed systematic Nuclear Magnetic Resonance (NMR) and magnetic susceptibility experiments in CeCuSb_22 single-crystals. The main findings were compared to previous report for CeCuBi_22. The NMR spectra and transferred hyperfine coupling for the ^{63}63Cu nuclei were obtained aiming to observe their correlation with the crystal electric field (CEF) effects on the Ce^{3+}3+ (J=5/2J=5/2) multiplet. Besides, in an attempt to elucidate the magnetic structure through NMR measurements at different magnetic fields orientations, we observed a magnetic transition at T\approx 8\,T≈8K higher than the Néel temperature T_NTN measured by magnetic susceptibility indicating the development of short-range magnetic ordering above T_NN. In addition, the wipe out of the main NMR resonance line and a persistent spin-echo signal throughout the whole frequency-swept range suggest the possibility of an incommensurate magnetic structure in CeCuSb_22. Furthermore, the small transferred hyperfine coupling constant found for CeCuSb_22 indicates a scenario with more localized Ce^{3+}3+ 4f electrons than for CeMIn_55 (M == Co,Rh,Ir) heavy fermions family. Additionally, subtle changes in the hybridization between the ^{63}63Cu with the 4f^11 Ce^{3+}3+ electrons in distinct magnetic field orientations allowed us to provide detailed information and map out the 4f CEF orbital ground-state of CeCu(Sb,Bi)_22 via NMR measurements.