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 \mu m ) .

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 \times 10 ^ { 21 } cm ^ { -2 } and v _ { k } \sin { i } =113 km/s .
The extinction properties of the dimming layer were derived with the effective optical depth ranging from \tau _ { eff } \sim 2.5-1.5 from the UV to the near-IR .
The inferred mass accretion rate \mathrm { \dot { M } _ { acc } } is \sim 1.5 \times 10 ^ { -8 } M _ { \odot } /yr and \sim 2 \times 10 ^ { -8 } M _ { \odot } /yr 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 .