  Motivated by the anomalous temperature dependence of the c-axis resistivity
of Sr$_2$RuO$_4$, the dimensional crossover from a network of perpendicular
one-dimensional chains to a two-dimensional system due to a weak hybridization
between the perpendicular chains is studied. The corresponding two-orbital
Hubbard model is treated within a slave-boson mean-field theory (SBMFT) to take
correlation effects into account such as the spin-charge separation on the
one-dimensional chains. Using an RPA-like formulation for the Green's function
of collective spinon-holon excitations the emergence of quasiparticles at
low-temperatures is examined. The results are used to discuss the evolution of
the spectral density and the c-axis transport within a tunneling approach. For
the latter a regime change between low- and high-temperature regime is found in
qualitative accordance with experimental data.
