I had a friend who helped conduct a study for an atheist group that looked into near death experiences. The group's aim was to dispel claims of the patient seeing himself or herself from above at some point during these experiences by placing objects in the room in positions that could only be seen from above and repeating random words to determine if they had hearing. AFAIK the study was unable to actually find someone with a near death experience.
Yeah, I remember hearing about such a study on the radio, tho it might have been a different one. Part of the problem is that the situations under which near death experiences happen and then the patient recovers enough to report on it are rare to begin with, and then not everyone who experiences them reports having such experiences, let alone the hovering version. Add to that the difficulty of having the difficulty of having all this happen where they re ready to conduct such a test, it is no wonder they've had a time just getting the conditions to test the phenomenon be done.