  We study the Hubbard model on a bilayer with repulsive on-site interactions,
$U$, in which fermions undergo both intra-plane ($t$) and inter-plane ($t_z$)
hopping. This situation is what one would expect in high-temperature
superconductors such as YBCO, with two adjacent CuO$_2$ planes. Magnetic and
pairing properties of the system are investigated through Quantum Monte Carlo
simulations for both half- and quarter-filled bands. We find that in all cases
inter-planar pairing with $d_{x^2-z^2}$ symmetry is dominant over planar
pairing with $d_{x^2-y^2}$ symmetry, and that for $t_z$ large enough pair
formation is possible through antiferromagnetic correlations. However, another
mechanism is needed to make these pairs condense into a superconducting state
at lower temperatures. We identify the temperature for pair formation with the
spin gap crossover temperature. [Submitted to Phys. Rev. B]
