We present the host galaxy molecular gas properties of a sample of 213 nearby (0.01<z< 0.05) hard X-ray selected AGN galaxies, drawn from the 70-month catalog of Swift-BAT, with 200 new CO(2-1) line measurements obtained with the JCMT and APEX telescopes. We find that AGN in massive galaxies tend to have more molecular gas, and higher gas fractions, than inactive galaxies matched in stellar mass. When matched in star formation, we find AGN galaxies show no difference from inactive galaxies with no evidence of AGN feedback affecting the molecular gas. The higher molecular gas content is related to AGN galaxies hosting a population of gas-rich early types with an order of magnitude more molecular gas and a smaller fraction of quenched, passive galaxies (~5% vs. 49%). The likelihood of a given galaxy hosting an AGN (L_bol>10^44 erg/s) increases by ~10-100 between a molecular gas mass of 10^8.7 Msun and 10^10.2 Msun. Higher Eddington ratio AGN galaxies tend to have higher molecular gas masses and gas fractions. Higher column density AGN galaxies (Log NH>23.4) are associated with lower depletion timescales and may prefer hosts with more gas centrally concentrated in the bulge that may be more prone to quenching than galaxy wide molecular gas. The significant average link of host galaxy molecular gas supply to SMBH growth may naturally lead to the general correlations found between SMBHs and their host galaxies, such as the correlations between SMBH mass and bulge properties and the redshift evolution of star formation and SMBH growth.
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