Context. Molecular gas, which serves as the fuel for star formation, and its relationship with atomic gas are essential for understanding how galaxies regulate their star forming activities. Aims. We conducted IRAM 30 m observations of 23 nearby spiral galaxies as part of the CHANG-ES project to investigate the distribution of molecular gas and the Kennicutt–Schmidt star formation law in these galaxies. By combining these results with atomic gas masses studied in previous work, we aim to investigate the scaling relations that connect the molecular and atomic gas masses with stellar masses and the baryonic Tully-Fisher relation. Methods. Based on spatially resolved observations of the 12CO J = 1 − 0, 13CO J = 1 − 0, and 12CO J = 2 − 1 molecular lines, we calculated the total molecular gas masses, obtained the ratios between different CO lines, and derived some key physical parameters, such as the temperature and optical depth of the molecular gas. Results. For the nuclear and disc regions, the median values of the 12CO/13CO J = 1 − 0 line ratio are 8.6 and 6.1, respectively, while those of the 12CO J = 2 − 1/J = 1 − 0 line ratio are 0.53 and 0.39. The molecular gas mass derived from 13CO J = 1 − 0 is strongly correlated with but systematically lower than that derived from 12CO J = 1 − 0. Most of the galaxies in our sample follow the spatially resolved star forming scaling relation between the star formation rate surface density and molecular gas mass surface density, with a median gas depletion time scale of ∼1 Gyr. A few galaxies exhibit enhanced star formation efficiency, with shorter time scales of ∼0.1 Gyr. Our sample shows a weak correlation between molecular and atomic gas but a strong correlation between the molecular-to-atomic gas mass ratio (MH2/MHI) and stellar mass, consistent with previous studies. Galaxies with lower stellar masses in our sample exhibit an excess of atomic gas by one magnitude compared to molecular gas, suggesting that the transformation of atomic gas into molecular gas is less efficient. Most galaxies tightly follow the baryonic Tully-Fisher relation, but NGC 2992 and NGC 4594 deviate from the relation due to different physical factors. We find that the ratio of the cold gas (comprising molecular and atomic gas) to the total baryon mass decreases with the gravitational potential of the galaxy, as traced by rotation velocity, which could be due to gas consumption in star formation or being heated to the hot phase.