A line from the the test point to the closest point on the curve will be perpendicular to the curve, if the curve is C1 (tangency) continuous and the closest point is not at the end of the curve. In regular Rhino the closest point can be found using ClosestPt.
If the closest point is at the end of the curve then a line between the test point and the closest point may or may not be perpendicular to the curve.
There may be additional points on the curve than the closest point for which a line between the test point and the point on the curve will be perpendicular to the curve. Each of these points will be the closest point to the test point for some portion of the curve.
If the curve has a kink and is therefore not C1 continuous then the closest point may be at a kink.