The molecular hydrogen content of a galaxy is a key parameter for its activity and future evolution. Its variations with basic properties such as size, mass, morphological type, and environment, the ratio of molecular to atomic gas masses, should provide us with a better view of galaxy evolution. Such studies have been done in the past by Sage (
1993A&A...272..123S) or the FCRAO group (e.g. Young & Knezek 1989), and have led to controversial results, for example about the M
H2/M
HI ratio. While Sage (
1993A&A...272..123S), using a distance-limited sample of 65 galaxies and the CO(1-0)line emission as a tracer of the H
2 mass, finds that most galaxies have M
H2/M
HI lower than 1, Young & Knezek (
1989ApJ...345L..55S) and Young et al. (
1995ApJS...98..219Y), from a different sample of 178 objects, claim equal amounts of gas in the molecular and atomic phase. Here we again tackle this problem, by gathering a much larger sample of 582 objects, not only from the literature but also from several CO(1-0)surveys that we have completed and which are largely unpublished. Our sample is clearly not complete and contains a large number of cluster galaxies as well as many more massive objects than a distance-limited sample. Contrary to previous analyses, we have taken into account the non-detections by using the survival analysis method. Our sample includes 105 isolated galaxies, observed by us, that we use as a reference sample in order to determine whether cluster galaxies are CO-deficient. We find that the ratio of H
2 and HI masses is on the average lower than 1, with <log(M
H2/M
HI)≥log(0.20)±0.04 (median=log(0.27)±0.04). For spirals with types Sa to Sc, we have slightly higher values: log(0.28) and log(0.34) respectively. The actual H
2 masses and M
H2/M
HI ratios could be lower than given above if, as suggested by recent γ-ray and 1.3mm continuum data, the conversion factor between CO(1-0)emissivities and H
2 masses for large spiral galaxies is lower than the value adopted here (X=2.3x10
20cm
–2/(K.km/s)). The molecular to atomic gas ratio shows a constant value from Sa to Sbc's, and a factor of 10 decrease for late-types, beginning at Sc's. This effect can be attributed to the low CO emission of late-type, low-mass galaxies; we find no such decrease for objects with a dynamical mass larger than 10
11M
☉. These high-mass objects actually show an increase of their normalized atomic and molecular gas content towards late-types, while for low-mass objects, this is seen on HI only. Several authors have tried to search for galaxies deficient in H
2 in the core of clusters such as Virgo or Coma, but these studies were hampered by the lack of a suitable reference sample (Kenney & Young
1989ApJ...344..171K, Casoli et al.
1991A&A...249..359C, Horellou et al.
1995A&A...303..361H). Using isolated galaxies and galaxies in the outer regions of clusters as a reference sample, we give a predictor for the normalized H
2 mass of a galaxy M
H2i/D
252, which depends upon its normalized far-infrared emission L
FIR/D
252 and its morphological type. This predictor allows us to define a ``CO deficiency factor'', CODEF, analogous to what has been defined for the HI emission. We find that there is no significant CO deficiency of galaxies in the cores of rich clusters.