I have a prefab crate which has the DragRigidbody behavior attached to it. If I have only one crate on the scene, dragging and dropping it is absolutely perfect. As I start adding crates however, I noticed that while dragging still works, dropping a crate causes it to stay mid-air for a long period if time. It still fals, but for a 10 times larger period ... it basically floats mid-air. Although I am a Unity newbie, I have developed games before, so I assume that there must be some kind of a controller that determines whether an object is being dragged. If there is one, the controller, must go through all the other crates and turn their Drag behavior off until the "active" crate is back on the floor. If there's something I'm missing ... a better way to do it, for instance, I will e glad to know about it.
Okay. It think I had mistaken the whole idea of the DragRigidbody. The DragRigidbody behavior is supposed to be instantiated once for the entire scene. Once I took it out of the crate prefab, and placed it on a single empty GameObject, residing in the scene, issues with the multiple rigid bodies disappeared completely. What I did have to look at from the very beginning was the script's source code :)