  We present an exact diagonalization study of bilayer clusters of t-J model.
Our results indicate a crossover between two markedly different regimes which
occurs when the ratio J_perp/J between inter-layer and intra-layer exchange
constants increases: for small J_perp/J the data suggest the development of 3D
antiferromagnetic correlations without appreciable degradation of the
intra-layer spin order and the d_(x2-y2) hole pairs within the planes persist.
For larger values of J_perp/J local singlets along the inter-layer bonds
dominate, leading to an almost complete suppression of the intra-layer spin
correlation and the breaking of the intra-layer pairs. The ground state with
two holes in this regime has s-like symmetry. The data suggest that the
crossover may occur for values of J_perp/J as small as 0.2. We present data for
static spin correlations, spin gap, and electron momentum distribution and
spectral function of the `inter-layer RVB state' realized for large J_perp/J.
The latter deviates from the single layer ground state, making it an
implausible candidate for modelling high-temperature superconductors.
