  We study the deformed complex Ginibre ensemble $H=A_0+H_0$, where $H_0$ is
the complex matrix with iid Gaussian entries, and $A_0$ is some general
$n\times n$ matrix (it can be random and in this case it is independent of
$H_0$). Assuming rather general assumptions on $A_0$, we prove that the
asymptotic local behavior of the second correlation function of the eigenvalues
of such matrices in the bulk coincides with that for the pure complex Ginibre
ensemble.
