Context. RW Aur A is a classical T Tauri star that has suddenly undergone three major dimming events since 2010. The reason for these dimming events is still not clear. Aims. We aim to understand the dimming properties, examine accretion variability, and derive the physical properties of the inner disc traced by the CO ro-vibrational emission at near-infrared wavelengths (2.3 μm). Methods. We compared two epochs of X-shooter observations, during and after the dimming. We modelled the rarely detected CO bandhead emission in both epochs to examine whether the inner disc properties had changed. The spectral energy distribution was used to derive the extinction properties of the dimmed spectrum and compare the infrared excess between the two epochs. Lines tracing accretion were used to derive the mass accretion rate in both states. Results. The CO originates from a region with physical properties of T = 3000 K, N_CO = 1 × 10²¹ cm⁻² and v_k sin i = 113 km s⁻¹. The extinction properties of the dimming layer were derived with the effective optical depth ranging from τ_eff ~2.5−1.5 from the UV to the near-IR. The inferred mass accretion rate Ṁ_acc is ~1.5 × 10⁻⁸ M_⊙ yr⁻¹ and ~2 × 10⁻⁸ M_⊙ yr⁻¹ after and during the dimming respectively. By fitting the spectral energy distribution, additional emission is observed in the infrared during the dimming event from dust grains with temperatures of 500–700 K. Conclusions. The physical conditions traced by the CO are similar for both epochs, indicating that the inner gaseous disc properties do not change during the dimming events. The extinction curve is flatter than that of the interstellar medium, and large grains of a few hundred microns are thus required. When we correct for the observed extinction, the mass accretion rate is constant in the two epochs, suggesting that the accretion is stable and therefore does not cause the dimming. The additional hot emission in the near-IR is located at about 0.5 au from the star and is not consistent with an occulting body located in the outer regions of the disc. The dimming events could be due to a dust-laden wind, a severe puffing-up of the inner rim, or a perturbation caused by the recent star-disc encounter.