One option: switch to modeling and create an associative "measure distance" feature with the "create output geometry" option toggled on; use the line or points to create your dimension in drafting then hide the measurement objects.
I believe if you are using Rapid Dimension, you can change the Measurement Method pulldown to Point to Point and make sure your Snap Point setting has Tangent Point enabled. This will work for arcs and most splines.
NX 18.104.22.168 MP11 Rev. A
GM TcE v22.214.171.124
GM GPDL v11-A.3.5.1
What about expressions -> measure distance?
Is there a solution that leaves geometry (line or points) that you can dimension to?
Production: NX10.0.3.5 MP16/TC11.2
I'd rather be e-steamed than e-diseaseled
Similar to what @cowski1 and @Ken_A suggested - create a sketch in the view on the drawing sheet. Construct lines such that their end points are tangent to the objects being measured and parallel to each other. Draw a line between the end points and use this to drive your dimension and then hide the sketch by clicking the checkbox under the view in the Part Navigator (part attached). Compare your result to the Distance Measurement "Minimum Distance" command.