ABSTRACT We investigate how the spectral properties of atomic (H i) and molecular (H2) gas, traced by CO(2−1) , are related in M33 on 80 pc scales. We find the H i and CO(2−1) velocity at peak intensity to be highly correlated, consistent with previous studies. By stacking spectra aligned to the velocity of H i peak intensity, we find that the CO line width (σHWHM = 4.6 ± 0.9 ${\rm km\, s^{-1}}$ ; σHWHM is the effective Gaussian width) is consistently smaller than the H i line width (σHWHM = 6.6 ± 0.1 ${\rm km\, s^{-1}}$), with a ratio of ∼0.7, in agreement with Druard et al. The ratio of the line widths remains less than unity when the data are smoothed to a coarser spatial resolution. In other nearby galaxies, this line width ratio is close to unity which has been used as evidence for a thick, diffuse molecular disc that is distinct from the thin molecular disc dominated by molecular clouds. The smaller line width ratio found here suggests that M33 has a marginal thick molecular disc. From modelling individual lines of sight, we recover a strong correlation between H i and CO line widths when only the H i located closest to the CO component is considered. The median line width ratio of the line-of-sight line widths is 0.56 ± 0.01. There is substantial scatter in the H i –CO(2−1) line width relation, larger than the uncertainties, that results from regional variations on <500 pc scales, and there is no significant trend in the line widths, or their ratios, with galactocentric radius. These regional line width variations may be a useful probe of changes in the local cloud environment or the evolutionary state of molecular clouds.