  Having to have low thermal energy, the molecular gas in galaxies is expected
to settle in a thin disc near the midplane. However, contradicting this
understanding, recent studies have revealed considerably thick molecular discs
in nearby spiral galaxies. To understand this apparent discrepancy, we
theoretically model the molecular discs in a sample of eight nearby spiral
galaxies and estimate their molecular scale heights (Half Width at Half Maxima
(HWHM)). We assume that the baryonic discs are in vertical hydrostatic
equilibrium under their mutual gravity in the external force field of the dark
matter halo. We set up the joint Poisson's-Boltzman equation of hydrostatic
equilibrium and numerically solve it to obtain the three-dimensional molecular
gas distribution and determine the scale heights in our sample galaxies. We
find that the scale heights follow a universal exponential law with a scale
length of $0.46 \pm 0.01 \ r_{25}$. The molecular scale heights in our sample
galaxies are found to vary between 50-200 pc depending on the galaxy and
radius. Using the density solutions, we build dynamical models of the molecular
discs and produce molecular column density maps. These model maps found to
match to the observed ones reasonably well. We further incline the dynamical
models to an inclination of 90$^o$ to estimate the expected observed thickness
of the molecular discs. Interestingly it is found that at edge-on orientation,
our sample galaxies under hydrostatic assumption can easily produce a few kpc
thick observable molecular disc.
