We consider a complex Ginibre ensemble of random matrices with a deformation $H=H_0+A$, where $H_0$ is a Gaussian complex Ginibre matrix and $A$ is a rather general deformation matrix. The analysis of such ensemble is motivated by many problems of random matrix theory and its applications. We use the Grassmann integration methods to obtain integral representation of spectral correlation functions of the first and the second  order and discuss the analysis of these representations with  a saddle point method. Applications  of such an analysis to the problems of local regime of the deformed Ginibre ensemble  will be discussed.