  The paper is concerned with the correlation functions of the characteristic
polynomials of random matrices with independent complex entries. We investigate
how the asymptotic behavior of the correlation functions depends on the second
moment of the common probability law of the matrix entries, a sort of ``reality
measure'' of the entries. It is shown that the correlation functions behave
like that for the Complex Ginibre Ensemble up to a factor depending only on the
second moment and the fourth absolute moment of the common probability law of
the matrix entries.
