Your statue lady might be a boo hag. They are from a Gullah legend, from the Carolinas and Georgia, originally brought over from Africa by slaves. But there are probably equivalents all over the world. A boo hag is a creature that sheds its skin and travels as a spirit at night. It sits on you while you sleep, gives you nightmares, and feeds on your energy.

A boo hag can get in through an open window or any little crack. It doesn't like a certain shade of blue (look up "haint blue") and you can repel it by painting the top of your windows that color. Also blue glass bottles hung from a tree are said to trap evil spirits.