RW Aur A is a CTTS that has suddenly undergone three major dimming events since 2010. 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 NIR wavelengths (2.3 mic). 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 SED 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. The CO originates from a region with physical properties of T=3000 K, N$_{CO}$=1x10$^{21}$ cm$^{-2}$ and vsini=113 km/s. The extinction properties of the dimming layer were derived with the effective optical depth ranging from teff 2.5-1.5 from the UV to the NIR. The inferred mass accretion rate Macc is $1.5x 10^{-8}$ Msun/yr and $sim 2x 10^{-8}$ Msun/yr after and during the dimming respectively. By fitting the SED, additional emission is observed in the IR during the dimming event from dust grains with temperatures of 500-700K. 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 ISM, and large grains of a few hundred microns are thus required. When we correct for the observed extinction, Macc 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 NIR is located at about 0.5 au from the star. 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.
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