  We investigate the statistical properties of the eigenvalues and eigenvectors
in a random matrix ensemble with $H_{ij}\sim |i-j|^{-\mu}$. It is known that
this model shows a localization-delocalization transition (LDT) as a function
of the parameter $\mu$. The model is critical at $\mu=1$ and the eigenstates
are multifractals. Based on numerical simulations we demonstrate that the
spectral statistics at criticality differs from semi-Poisson statistics which
is expected to be a general feature of systems exhibiting a LDT or `weak
chaos'.
