Context. We report the results from the determination of stellar masses, carbon, and oxygen abundances in the atmospheres of 107 stars from the Calan-Hertfordshire Extrasolar Planet Search (CHEPS) programme. Our stars are drawn from a population with a significantly super-solar metallicity. At least 10 of these stars are known to host orbiting planets. Aims. In this work, we set out to understand the behaviour of carbon and oxygen abundance in stars with different spectral classes, metallicities, and V sin i within the metal-rich stellar population. Methods. Masses of these stars were determined using data from Gaia DR2. Oxygen and carbon abundances were determined by fitting the absorption lines. We determined oxygen abundances with fits to the 6300.304 Å O I line, and we used 3 lines of the C I atom and 12 lines of the C₂ molecule for the determination of carbon abundances. Results. We determine masses and abundances of 107 CHEPS stars. There is no evidence that the [C/O] ratio depends on V sin i or the mass of the star within our constrained range of masses, i.e. 0.82 < M_*∕M_⊙ < 1.5 and metallicities − 0.27 < [Fe∕H] < +0.39. We also confirm that metal-rich dwarf stars with planets are more carbon rich in comparison with non-planet host stars with a statistical significance of 96%. Conclusions. We find tentative evidence that there is a slight offset to lower abundance and a greater dispersion in oxygen abundances relative to carbon. We interpret this as potentially arising because the production of oxygen is more effective at more metal-poor epochs. We also find evidence that for lower mass stars the angular momentum loss in stars with planets as measured by V sin i is steeper than stars without planets. In general, we find that the fast rotators (V sin i > 5 km s⁻¹) are massive stars.