We study the properties of the cold gas component of the interstellar medium of the Herschel Reference Survey, a complete volume-limited (15 ≲ D ≲ 25 Mpc), K-band-selected sample of galaxies spanning a wide range in morphological type (from ellipticals to dwarf irregulars) and stellar mass (109 ≲ Mstar ≲ 1011 Mstar. The multifrequency data in our hands are used to trace the molecular gas mass distribution and the main scaling relations of the sample, which put strong constraints on galaxy formation simulations. We extend the main scaling relations concerning the total and the molecular gas component determined for massive galaxies (Mstar ≳ 1010 M⊙) from the COLD GASS survey down to stellar masses Mstar ≃ 10 9M⊙. As scaling variables we use the total stellar mass Mstar, the stellar surface density μstar, the specific star formation rate SSFR, and the metallicity of the target galaxies. By comparing molecular gas masses determined using a constant or a luminosity dependent XCO conversion factor, we estimate the robustness of these scaling relations on the very uncertain assumptions used to transform CO line intensities into molecular gas masses. The molecular gas distribution of a K-band-selected sample is significantly different from that of a far-infrared-selected sample since it includes a significantly smaller number of objects with M(H2) ≲ 6 × 109 M ⊙. In spiral galaxies the molecular gas phase is only 25-30% of the atomic gas. The analysis also indicates that the slope of the main scaling relations depends on the adopted conversion factor. Among the sampled relations, all those concerning M(gas)/Mstar are statistically significant and show little variation with XCO. We observe a significant correlation between M(H2)/Mstar and SSFR, M(H2)/M(Hi) and μstar, M(H2)/M(Hi) and 12+log+(O/H), regardless of the adopted XCO. The total and molecular gas consumption timescales are anticorrelated with the specific star formation rate. The comparison of HRS and COLD GASS data indicates that some of the observed scaling relations are nonlinear. © 2014 ESO .