  We investigate the spectral statistics of a network model for a three
dimensional layered quantum Hall system numerically. The scaling of the
quantity $J_0={1/2}< s^2>$ is used to determine the critical exponent $\nu$ for
several interlayer coupling strengths. Furthermore, we determine the level
spacing distribution $P(s)$ as well as the spectral compressibility $\chi$ at
criticality. We show that the tail of $P(s)$ decays as $\exp(-\kappa s)$ with
$\kappa=1/(2\chi)$ and also numerically verify the equation
$\chi=(d-D_2)/(2d)$, where $D_2$ is the correlation dimension and $d=3$ the
spatial dimension.
