We consider a multidimensional stochastic differential equation Y written as a drift-perturbation of an ergodic Ornstein-Uhlenbeck process X. Under the condition of time-reversibility of X, we derive a first and second order expansion of the stationary distribution µ^Y of Y in terms of X. Error estimates are established. These approximations are then turned into a simulation scheme for sampling approximately according to µ Y. Numerical experiments support the theoretical error estimates.