The pic makes it look as though the co-op also has a flat roof? This isnt good either, I would think that if there is nowhere for run-off and no guttering the water may seep down the adjoining wall which is where it is damp. If its wetter at the bottom tho it does suggest rising damp, there may be no damp proof membrane in the subfloor. Some old buldings used slate and this will have had a limited lifespan. (can u tell I used to type survey reports? lol)
You need a preservation surveyor to give an expert opinion, some will do this free, ask around.