It is illegal for a joint to connect a rigid body to itself. UnityEngine.Joint:set_connectedBody(Rigidbody)

Questions & Answers
1

Although I figured this out, I’ll post the answer here to help other save a few minutes

How can I add CharacterJoint at runtime and assign it a rigidbody? This error comes up but how else should a rigidbody be assigned?

//We have a rigidbody on this gameobject
CharacterJoint j = gameObject.AddComponent();
j.connectedBody = r;

2

The characterjoint is always linking to a rigidbody on another gameobject (parent/child/whatever).
The characterjoint may indeed not connect to the GO’s rigidody itself since that it what it represents itself. The connectedBody must be an outside connection.