Boundary layer problems (Singular perturbation problems) more have been applied for ordinary differential equations. While this theory for partial differential equations have many applications in several fields of physics and engineering. Because of complexity of limit and boundary behavior of the solutions of partial differential equations these problems considered less than ordinary case. In this paper, a boundary layer problem including perturbed Cauchy- Riemann equation is considered with a non local boundary condition. For the given problem , some sufficient conditions will be presented so that the problem be well posed and without any boundary layer. In this case, the approximate solutions of the problem can be written same as boundary layer problems for ordinary differential equations