Compact radio galaxies with a GHz-peaked spectrum ( GPS ) and/or compact-symmetric-object ( CSO ) morphology ( GPS/CSOs ) are increasingly detected in the X-ray domain . Their radio and X-ray emissions are affected by significant absorption . However , the locations of the X-ray and radio absorbers are still debated . We investigated the relationship between the column densities of the total ( N _ { \mathrm { H } } ) and neutral ( N _ { \mathrm { HI } } ) hydrogen to statistically constrain the picture . We compiled a sample of GPS/CSOs including both literature data and new radio data that we acquired with the Westerbork Synthesis Radio Telescope for sources whose X-ray emission was either established or under investigation . In this sample , we compared the X-ray and radio hydrogen column densities , and found that N _ { \mathrm { H } } and N _ { \mathrm { HI } } display a significant positive correlation , with N _ { \mathrm { HI } } \propto N _ { \mathrm { H } } ^ { b } , where b = 0.47 and b = 0.35 , depending on the subsample . The N _ { \mathrm { H } } - N _ { \mathrm { HI } } correlation suggests that the X-ray and radio absorbers are either co-spatial or different components of a continuous structure . The correlation displays a large intrinsic spread that we suggest to originate from fluctuations , around a mean value , of the ratio between the spin temperature and the covering factor of the radio absorber , T _ { s } / C _ { f } .