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 E to Im) and stellar mass (10^9<M*<10^11 Mo). 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 (M* > 10^10 Mo) from the COLD GASS survey down to stellar masses M* ~ 10^9 Mo. As scaling variables we use M*, the stellar surface density mu*, 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 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 different from that of a far-infrared-selected sample since it includes a significantly smaller number of objects with M(H2) < 6 10^9 Mo. 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)/M* are statistically significant and show little variation with X_CO. We observe a significant correlation between M(H2)/M* and SSFR, M(H2)/M(HI) and mu*, M(H2)/M(HI), and 12+log(O/H) regardless of the adopted X_CO. The total and molecular gas consumption timescales are anticorrelated with the SSFR.
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