  We measure the molecular-to-atomic gas ratio, $R_{\rm mol}$, and the star
formation rate (SFR) per unit molecular gas mass, SFE$_{\rm mol}$, in 38 nearby
galaxies selected from the Virgo Environment Traced in CO (VERTICO) survey. We
determine their scale-lengths for the molecular and stellar components and find
a roughly 3:5 ratio between them compared to $\sim$1:1 in field galaxies,
indicating that the CO emission is more centrally concentrated than the stars.
We compute $R_{\rm mol}$ as a function of different physical quantities. While
the spatially-resolved $R_{\rm mol}$ on average decreases with increasing
radius, we find that the mean molecular-to-atomic gas ratio within the stellar
effective radius $R_{\rm e}$, $R_{\rm mol}(r<R_{\rm e})$, shows a systematic
increase with the level of H$_{\rm I}$, truncation and/or asymmetry (H$_{\rm
I}$ perturbation). Analysis of the molecular- and the atomic-to-stellar mass
ratios within $R_{\rm e}$, $R^{\rm mol}_{\star}(r<R_{\rm e})$ and $R^{\rm
atom}_{\star}(r<R_{\rm e})$, shows that VERTICO galaxies have increasingly
lower $R^{\rm atom}_{\star}(r<R_{\rm e})$ for larger levels of H$_{\rm
I}$perturbation (compared to field galaxies matched in stellar mass), but no
significant change in $R^{\rm mol}_{\star}(r<R_{\rm e})$. We also measure a
clear systematic decrease of the SFE$_{\rm mol}$ within $R_{\rm e}$, SFE$_{\rm
mol}(r<R_{\rm e})$, with increasingly perturbed H$_{\rm I}$. Therefore,
compared to galaxies from the field, VERTICO galaxies are more compact in CO
emission in relation to their stellar distribution, but increasingly perturbed
atomic gas increases their $R_{\rm mol}$ and decreases the efficiency with
which their molecular gas forms stars. (abridged)
