  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.
