We study the electronic structure of CeCuAs2, which is known to show an anomalous negative temperature coefficient of resistivity below room temperature, while the thermopower shows metallic behavior. We carry out hard x-ray photoemission spectroscopy (PES), x-ray absorption spectroscopy (XAS), and resonant PES across the Ce 3d-4f and Cu 2p-3d thresholds to investigate the role of Kondo screening in CeCuAs2. The Ce 3d core-level PES shows the f(0), f(1), and f(2) features, and the Ce 3d-4f XAS shows corresponding features due to transitions into the f(1) and f(2) states, as in Kondo systems. The spectral feature assignments are confirmed by single-impurity Anderson model calculations and indicate a nearly trivalent-Ce configuration with small but finite mixed valency. The resonant PES valence band spectra across the Ce 3d-4f threshold show an intense Ce 4f(1) resonance just below the Fermi level, while the Ce 4f(0) feature is observed at a binding energy of 2.5 eV. The obtained f partial density of states shows an unusual pseudogaplike dip at the Fermi level in CeCuAs2. The results indicate the importance of Kondo screening and a pseudogap in the f partial density of states for the anomalous transport and magnetic properties of CeCuAs2.