We discuss the relative abundance of CI / H2 in the diffuse cold neutral medium. Using semi-analytical formalism, we describe how CI / H2 depends on the main parameters of the medium: number density, metallicity, strength of the UV field and cosmic ray ionization rate. We show that observed relative abundance of CI / H2 in the high-redshift damped Lyman alpha systems can be reproduced within our model assuming the typical expected conditions in the diffuse cold medium. We also discuss that the observed relative abundance of CI / H2, when coupled with data on the population of the fine structure levels of neutral carbon and the rotational levels of molecular hydrogen can be used to derive the cosmic ray ionization rate in the low-metallicity interstellar medium.