  We investigate numerically the statistical properties of spectra of
two-dimensional disordered systems by using the exact diagonalization and
decimation method applied to the Anderson model. Statistics of spacings
calculated for system sizes up to 1024 $\times$ 1024 lattice sites exhibits a
crossover between Wigner and Poisson distributions. We perform a self-contained
finite-size scaling analysis to find a single-valued one-parameter function
$\gamma (L/\xi)$ which governs the crossover. The scaling parameter $\xi(W)$ is
deduced and compared with the localization length. $\gamma ( L/\xi)$ does {\em
not} show critical behavior and has two asymptotic regimes corresponding to
weakly and strongly localized states.
