The identification problem of the limit of an ODE with non-Lipschitz drift perturbed by a zero-noise is considered in a multidimensional framework. This problem is a classical subject of stochastic analysis, however the multidimensional case was poorly investigated. We consider two cases in particular: (i) the drift coefficient has a jump discontinuity along an hyperplane and is Lipschitz continuous in the upper and lower half-spaces; (ii) the drift is equivalent to a (phi) r^\alpha as r tends to 0, where (r,phi) are the polar coordinates, and \alpha < 1.