Cops now believe the children's book that was allegedly 'left' in her home ... was hers all along! As TMZ first reported, the X-Men star called NYPD back in August after she returned to her ritzy NYC pad and found a children's book called The Lonely Doll in her bedroom.

But now detectives think the book was hers because they found errand lists tucked in the pages of the book -- and Famke's name was reportedly on at least one of the notes. Police reportedly believe the book has some connection to Famke's home.