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We measure the molecular-to-atomic gas ratio,R_mol, and the star formation rate (SFR) per unit molecular gas mass, SFE_mol, in 38 nearby galaxies selected from the Virgo Environment Traced in CO (VERTICO) survey. We stack ALMA¹²CO (J= 2−1) spectra coherently using Hivelocities from the VIVA survey to detect faint CO emission out to galactocentric radiir_gal∼ 1.2r₂₅. We determine the scale lengths for the molecular and stellar components, finding a ∼3:5 relation compared to ∼1:1 in field galaxies, indicating that the CO emission is more centrally concentrated than the stars. We computeR_molas a function of different physical quantities. While the spatially resolvedR_molon average decreases with increasing radius, we find that the mean molecular-to-atomic gas ratio within the stellar effective radiusR_e,R_mol(r<R_e), shows a systematic increase with the level of Hi, truncation and/or asymmetry (H_Iperturbation). Analysis of the molecular- and the atomic-to-stellar mass ratios withinR_e,$R_{\star }^{\mathrm{mol}}(r<R_e)$and$R_{\star }^{\mathrm{atom}}(r<R_e)$, shows that VERTICO galaxies have increasingly lower$R_{\star }^{\mathrm{atom}}(r<R_e)$for larger levels of H_Iperturbation (compared to field galaxies matched in stellar mass), but no significant change in$R_{\star }^{\mathrm{m}\mathrm{o}\mathrm{l}}(r<R_e)$. We also measure a clear systematic decrease of the SFE_molwithinR_e, SFE_mol(r<R_e), with increasingly perturbed Hi. Therefore, compared to field galaxies from the field, VERTICO galaxies are more compact in CO emission in relation to their stellar distribution, but increasingly perturbed atomic gas increases theirR_moland decreases the efficiency with which their molecular gas forms stars.