I have had a similar event happen in my property. I have had 4 different residents report to me different incidences that occur in their unit. In one case, it actually got a little extreme... The resident asked for a transfer because they believed :S that there is a "demon" that is messing with a child in the house. Her description of everything sounded very scary. I suggested that she goes to a local church, and maybe have a priest "bless" the house. I was not too sure how to proceed with it, and my supervisor made me write an incident report, just case! :)
Unfortunately, I cannot fully say that I do not believe the residents. We have security cameras in the property, and one morning my playground was a mess. I decided to look at the security cameras to see if I could find the culprit, and low and behold, I saw a figure that closely resembles a ghost walking down the walk way!!! No kidding, I had to look at the image over and over again and eventually became convinced that it was a ghost that I saw. But... for my own sake, I have came to the conclusion that this image somehow was a mistake, a reflection of some sort, or something else. I have decided to elude my mind from thinking it is a ghost because I am a scary cat! And to top it off, I saw this image BEFORE the resident started to report the paranormal activities in the house. :S