  We consider the deformed Laguerre Ensemble
$H_n=\dfrac{1}{m}\Sigma_n^{1/2}A_{m,n}A_{m,n}^*\Sigma_n^{1/2}$ in which
$\Sigma_n$ is a positive hermitian matrix (possibly random) and $A_{m,n}$ is a
$n\times m$ complex Gaussian random matrix (independent of $\Sigma_n$),
$\dfrac{m}{n}\to c>1$. Assuming that the Normalized Counting Measure of
$\Sigma_n$ converges weakly (in probability) to a non-random measure $N^{(0)}$
with a bounded support we prove the universality of the local eigenvalue
statistics in the bulk of the limiting spectrum of $H_n$.
