  IRAM 30m 12CO(1-0) and 12CO(2-1) HERA observations are presented for the
ram-pressure stripped Virgo spiral galaxy NGC 4522. The CO emission is detected
in the galactic disk and the extraplanar gas. The extraplanar CO emission
follows the morphology of the atomic gas closely but is less extended. The CO
maxima do not appear to correspond to regions where there is peak massive star
formation as probed by Halpha emission. The presence of molecular gas is a
necessary but not sufficient condition for star formation. Compared to the disk
gas, the molecular fraction of the extraplanar gas is 30% lower and the star
formation efficiency of the extraplanar gas is about 3 times lower. The
comparison with an existing dynamical model extended by a recipe for
distinguishing between atomic and molecular gas shows that a significant part
of the gas is stripped in the form of overdense arm-like structures. It is
argued that the molecular fraction depends on the square root of the total
large-scale density. Based on the combination of the CO/Halpha and an
analytical model, the total gas density is estimated to be about 4 times lower
than that of the galactic disk. Molecules and stars form within this dense gas
according to the same laws as in the galactic disk, i.e. they mainly depend on
the total large-scale gas density. Star formation proceeds where the local
large-scale gas density is highest. Given the complex 3D morphology this does
not correspond to the peaks in the surface density. In the absence of a
confining gravitational potential, the stripped gas arms will most probably
disperse; i.e. the density of the gas will decrease and star formation will
cease.
