Why not take a garden hose and turn the water on, let it run in the hole and see if it a) fills up, or b) flows on down somewhere? If it flows away, it has to lead somewhere?
Is it possible the hole is an old hand-pump well that's been capped over?
I lived in a house that had a capped over hand-pump well. I ended up pouring another layer of concrete over the top, reinforced for wire and everything. I was afraid the concrete was too thin. With young kids at home, I didn't want to take any chances.
I also thought about putting in another hand pump, but I could shine a flashlight down that small hole in the middle of the concrete, and it was quite obvious a well, like you'd drop a bucket into a long time ago. I looked really bad. I couldn't see the value of a hand pump. I think at one time it was the primary water source to that house. But not no more. It was adapted to tap into a county water line. This was in SW Ohio.