A quantal study is carried out of the rotational excitation of carbon monoxide in collision with hydrogen atoms. The interaction potential at short range is constructed semi-empirically and joined to the Buckingham potential at long range. The close-coupling formulation is used to assess the reliability of the fixed-nuclei approximation, which is developed in terms of the adiabatic theory of electron-molecule scattering. The applicability of two simplified close-coupling formulations, introduced by Rabitz and by McGuire & Kouri, is examined. We found that the fixed nuclei method is unpromising at low energies and time-consuming at high energies. The two simplified close-coupling methods are capable of providing results of useful accuracy. The similarity in formulation of the fixed-nuclei and one of the close-coupling methods, both of which are body-frame treatments, and the differences in their results show that the rotational degree of freedom must be treated rigorously. The method of Rabitz is economical, and we adopted it to calculate the energy dependent rotation excitation cross sections for the scattering of H + CO. The results are presented in the form of Maxwellian-averaged rate coefficients in the temperature range of 5-150 K.