  Quasi-two-dimensional fluids can be generated by confining a fluid between
two parallel walls with narrow separation. Such fluids exhibit an inhomogeneous
structure perpendicular to the walls due to the loss of translational symmetry.
Taking the transversal degrees of freedom as a perturbation to an appropriate
2D reference fluid we provide a systematic expansion of the $m$-particle
density for arbitrary $m$. To leading order in the slit width this density
factorizes into the densities of the transversal and lateral degrees of
freedom. Explicit expressions for the next-to-leading order terms are
elaborated analytically quantifying the onset of inhomogeneity. The case $m=1$
yields the density profile with a curvature given by an integral over the
pair-distribution function of the corresponding 2D reference fluid, which
reduces to its 2D contact value in the case of pure excluded-volume
interactions. Interestingly, we find that the 2D limit is subtle and requires
stringent conditions on the fluid-wall interactions. We quantify the rapidity
of convergence for various structural quantities to their 2D counterparts.
