Blue compact dwarf galaxies (BCDGs) are currently undergoing strong bursts of
star formation. Nevertheless, only a few of them have been clearly detected in
CO, which is thought to trace the "fuel" of star formation: H_2. In this paper,
we present a deep search for CO J=1-->0 and J=2-->1 emission lines in a sample
of 8 BCDGs and two companions. Only 2 of them (Haro 2 and UM 465) are detected.
For the other galaxies we have obtained more stringent upper limits on the CO
luminosity than published values. We could not confirm the previously reported
``detection'' of CO for the galaxies UM 456 and UM 462. We analyze a possible
relation between metallicity, CO luminosity, and absolute blue magnitude of the
galaxies. We use previously determined relations between X = N(H_2)/I_CO and
the metallicity to derive molecular cloud masses or upper limits for them. With
these ``global'' X_CO values we find that for those galaxies which we detect in
CO, the molecular gas mass is similar to the HI mass, whereas for the
non-detections, the upper limits on the molecular gas masses are significantly
lower than the HI mass. Using an LVG (Large Velocity Gradient) model we show
that X_CO depends not only on metallicity, but also on other physical
parameters such as volume density and kinetic temperature, which rises the
question on the validity of ``global'' X_CO factors.Comment: 9 pages, 6 figures, to be published on MNRA