We investigate the magnetic and crystal electric field (CEF) states of the Kondo lattice system CeCuGa3 by muon spin relaxation (μSR), neutron diffraction, and inelastic neutron scattering (INS) measurements. A noncentrosymmetric BaNiSn3-type tetragonal crystal structure (space group I4mm) is inferred from x-ray as well as from neutron powder diffraction. The low-temperature magnetic susceptibility and heat capacity data show an anomaly near 2.3–2.5 K, associated with long-range magnetic ordering, which is further confirmed by μSR and neutron diffraction data. The neutron powder diffraction collected at 1.7 K shows the presence of magnetic Bragg peaks indexed by an incommensurate magnetic propagation vector k =(0.148,0.148,0) and the magnetic structure is best described by a longitudinal spin density wave with ordered moments lying in the ab-plane. An analysis of the INS data based on a CEF model reveals the presence of two magnetic excitations near 4.5 meV and 6.9 meV. The magnetic heat capacity data suggest an overall CEF splitting of 20.7 meV, however, the excitation between 20 and 30 meV is very broad and weak in our INS data, but could provide an evidence of CEF level in this energy range in agreement with the magnetic entropy. Our analysis of INS data based on the CEF-phonon model indicates that the two excitations at 4.5 meV and 6.9 meV have their origin in CEF-phonon coupling (i.e., splitting of one CEF peak into two peaks, called vibron), with an overall splitting of 28.16 meV, similar to the case of CeCuAl3 and CeAuAl3.