When I was a kid in the early 80's, I remember two of my female neighbor friends telling me about how they got freaked out by a movie where a girl is going either up or down the stairs with a pizza cutter.
They told me it was a movie titled, "
The Babysitter".
Here's the link:
http://www.imdb.com/title/tt0080407/Not sure if that's the one you're looking for but it sounds promising.