  We consider the asymptotic local behavior of the second correlation function
of the characteristic polynomials of sparse non-Hermitian random matrices $X_n$
whose entries have the form $x_{jk}=d_{jk}w_{jk}$ with iid complex standard
Gaussian $w_{jk}$ and normalised iid Bernoulli$(p)$ $d_{jk}$. It is shown that,
as $p\to\infty$, the local asymptotic behavior of the second correlation
function of characteristic polynomials near $z_0\in \mathbb{C}$ coincides with
those for Ginibre ensemble: it converges to a determinant with Ginibre kernel
in the bulk $|z_0|<1$, and it is factorized if $|z_0|>1$. For the finite $p>0$,
the behavior is different and exhibits the transition between three different
regimes depending on values of $p$ and $|z_0|^2$.
