We present (CO)-C-12(J=1-0) line observations of 73 spiral galaxies mo
stly in the Coma/A1367 supercluster. From these data, combined with da
ta available in the literature, we extract the first complete, optical
ly selected sample (m(pg) < 15.2) of 37 isolated and of 27 cluster gal
axies. Adopting a standard conversion factor X=N(H-2)/I(CO), we estima
te that the molecular hydrogen content of isolated spiral galaxies is,
on average, 20% of the atomic hydrogen reservoir, significantly lower
than previous estimates based on samples selected by FIR criteria, th
us biased towards CO rich objects. We show that the frequency distribu
tions of the CO deficiency parameter, defined as the difference betwee
n the expected and the observed molecular gas content of a galaxy of g
iven luminosity (or linear diameter), computed separately for cluster
and isolated galaxies, are not significantly different, indicating tha
t the environment does not affect the molecular gas content of spiral
discs. A well defined relationship exists between M-i(H-2) and the sta
r formation activity in bright galaxies, while it is weaker at lower l
uminosities. We interpret this finding as indicating that CO emission
traces relatively well the H-2 mass only in high-mass galaxies, such a
s the Milky Way. On the other hand, in low-mass spirals the higher far
-UV radiation field produced by young O-B stars and the lower metallic
ity cause the photodissociation of the diffuse molecular gas, weakenin
g the expected relationship between star formation and the CO emission
. The conversion factor between the CO line intensity and the amount o
f molecular hydrogen being ill-determined and variable with the UV flu
x and abundances, it is difficult to assess the relationship between t
he star formation and the amount of molecular hydrogen.