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We investigate how the spectral properties of atomic (HI) and molecular(H$_2$) gas, traced by CO(2-1), are related in M33 on $80$ pc scales. We findthe HI and CO(2-1) velocity at peak intensity to be highly correlated,consistent with previous studies. By stacking spectra aligned to the velocityof HI peak intensity, we find that the CO line width ($\sigma_{\rmHWHM}=4.6\pm0.9$ km s$^{-1}$; $\sigma_{\rm HWHM}$ is the effective Gaussianwidth) is consistently smaller than the HI line width ($\sigma_{\rmHWHM}=6.6\pm0.1$ km s$^{-1}$), with a ratio of ${\sim}0.7$, in agreement withDruard et al. (2014). The ratio of the line widths remains less than unity whenthe data are smoothed to a coarser spatial resolution. In other nearbygalaxies, this line width ratio is close to unity which has been used asevidence for a thick, diffuse molecular disk that is distinct from the thinmolecular disk dominated by molecular clouds. The smaller line width ratiofound here suggests that M33 has a marginal thick molecular disk. Frommodelling individual lines-of-sight, we recover a strong correlation between HIand CO line widths when only the HI located closest to the CO component isconsidered. The median line width ratio of the line-of-sight line widths is$0.56\pm0.01$. There is substantial scatter in the HI--CO(2-1) line widthrelation, larger than the uncertainties, that results from regional variationson $<500$ pc scales, and there is no significant trend in the line widths, ortheir ratios, with galactocentric radius. These regional line width variationsmay be a useful probe of changes in the local cloud environment or theevolutionary state of molecular clouds.

Relationship between the Line Width of the Atomic and Molecular ISM in M33