Aims. An analysis of the CH molecule in non-local thermodynamic equilibrium (NLTE) is performed for the physical conditions of cool stellar atmospheres typical of red giants (log g = 2.0, T e ff = 4500 K) and the Sun. The aim of the present work is to explore whether the G -band of the CH molecule, which is commonly used in abundance diagnostics of Carbon-Enhanced Metal-Poor (CEMP) stars, is sensitive to NLTE e ff ects. Methods. Local thermodynamic equilibrium (LTE) and NLTE theoretical spectra are computed with the MULTI code. We use one- dimensional (1D) LTE hydrostatic MARCS model atmospheres with parameters representing eleven red giant stars with metallicities ranging from [Fe / H] = − 4 . 0 to [Fe / H] = 0 . 0 and carbon-to-iron ratios [C / Fe] = 0.0, + 0.7, + 1.5, and + 3.0. The CH molecule model is represented by 1 981 energy levels, 18 377 radiative bound-bound transitions, and 932 photo-dissociation reactions. The rates due to transitions caused by collisions with free electrons and hydrogen atoms are computed using classical recipes. Results. Our calculations suggest that NLTE e ff ects in the statistical equilibrium of the CH molecule are significant and cannot be neglected for precision spectroscopic analysis of C abundances. The NLTE e ff ects are mostly driven by radiative over-dissociation, owing to the very low dissociation threshold of the molecule and significant resonances in the photo-dissociation cross-sections. The NLTE e ff ects in the G -band increase with decreasing metallicity. When comparing the C abundances determined from the CH G -band in LTE and in NLTE, we show that the C abundances are always under-estimated if LTE is assumed. The NLTE corrections to C abundance inferred from the CH feature range from + 0 . 04 dex for the Sun to + 0 . 21 dex for a red giant with metallicity [Fe / H] = − 4 . 0. Conclusions. Departures from the LTE assumption in the CH molecule are non-negligible and NLTE e ff ects have to be taken into account in the diagnostic spectroscopy based on the CH lines. We show here that the NLTE e ff ects in the optical CH lines are non-negligible for the Sun and red giant stars, but further calculations are warranted to investigate the e ff ects in other regimes of stellar parameters.