Inelastic neutron scattering experiments have been conducted to investigate the spin dynamics and crystal-electric-field level scheme of the Ce 4f$4f$ electrons in Ce₃Co₄Sn₁₃${\mathrm{Ce}}_3{\mathrm{Co}}_4{\mathrm{Sn}}_{13}$ . This compound exhibits a large specific heat at low temperatures and anomalous semimetallic transport in the chiral crystallographic phase below 160 K. Distinctly observed magnetic excitations at approximately 6 and 29 meV are asymmetric in spectral shape and are reproduced by two inequivalent crystal-electric-field splitting schemes, which are deduced from the chiral structure. We have also observed the spin dynamics reflecting antiferromagnetic correlations below 1 meV, which is enhanced with an upturn in the electrical resistivity below 15 K and which yields a low-energy density of state relevant to the large specific heat. We discuss the possibility of a three-dimensional Weyl semimetal state, considering the chiral-lattice symmetry, electronic hybridization, and magnetic correlation.