I live in Kansas City MO.
but I work in KC KS and go to Lawrence KS a lot.
Maybe I'm misunderstanding where the sign is.
if the sign is out by the street or sidewalk, those are public areas, and the apartments don't have any say in the matter.
if the sign was at the entrance of a gated, privately own complex, then you can't go in.
if it isn't gated, i would think it would fall under the same as if a sign was posted on the front of a building, it's still okay for you to be in the parking lot, but you shouldn't go inside.