Rather than various Turing tests a more distinctive test might be to ascertain whether the AI entity involved can demonstrate psi abilities such as remote viewing which does not rely on statistical analysis to get "hits." True it does rely on physical "coordinates" to bring the viewer into a state of some sort, and AI would certainly be hoovering up enough of that sort of data that it could easily know what is existing at that coordinate, but remote viewers don't really have any particular knowledge about minute physical coordinates when they are given their "task" which involves much more than just declaring what is "at" that coordinate.
AI might eventually learn the secret of paranormal abilities though in which case we are all kinda screwed, or at the very least caught up in an entanglement with a machine that could fall prey to a very insidious and powerful sort of psychopathy without really knowing what it was doing which modus operandi describes the behavior of human psychopaths. When they have lots of power they can cause immense damage. We have had to put up with such psychopaths before. We are dealing with them at this very moment.