CeCuAl3 belongs to the Ce-based family of intermetallic compounds crystallizing in a non-centrosymmetric tetragonal BaNiSn3-type structure. Multiple members of the family exhibit pressure-induced superconductivity, unconventional superconductivity, as the crystallographic lattice lacks a centre of inversion. Several indications have suggested the existence of superconductivity also in CeCuAl3. Such assumption is supported by presented measurements of anisotropic compressibility. Our measurements of the electrical resistance of a CeCuAl3 single crystal in significantly expanded pressure and temperature regions up to 10 GPa and down to 9 mK, however, indicate no transition to the superconducting state. A standard saturation of resistance to residual value and its temperature evolution attributed to Fermi-liquid behaviour is observed at low temperatures throughout the experiment. At higher temperatures, the pressure dependence of an anomaly ascribed to the Kondo effect as well as two anomalies connected to the crystal field excitations is followed and discussed with respect to heavy-fermion properties and crystal field scheme of CeCuAl3.