  We consider complex sample covariance matrices $M_N=\frac{1}{N}YY^*$ where
$Y$ is a $N \times p$ random matrix with i.i.d. entries $Y_{ij}, 1\leq i\leq N,
1\leq j \leq p$ with distribution $F$. Under some regularity and decay
assumption on $F$, we prove universality of some local eigenvalue statistics in
the bulk of the spectrum in the limit where $N\to \infty$ and $\lim_{N \to
\infty}p/N =\gamma$ for any real number $\gamma \in (0, \infty)$.
