In this paper, we study the problem of the asymptotic property of the norm of input-output operators related to a class of singularly perturbed stochastic linear systems. The system is under perturbation of multiplicative white noise. By using reduction order and boundary layer techniques, it is shown that the norm of the operator of the perturbed system is less than a given number gamma when the small perturbation tends to zero if both the related norms of the reduced subsystem and the boundary layer subsystem are less than gamma. Furthermore, a stabilizing robust controller is designed, which is independent of perturbation epsilon.