You can iterate through all transformed vertices of the object by using the PolygonManager, calculate the euclidean distance from your point in world space by yourself and take the lowest value as the distance (which is not always the shortest distance because it ignores that a polygon's plane can have a shorter distance than it's points, but it may be good enough).

Edit: Or you can use the IVertexController to get the vertices in object space and do the check there, after transforming your point into object space using the object's inverse world transformation...should be more efficient.