Diane and Greg, you are correct! It is indeed Thuja plicata or as I call it....Western Red Cedar - the crushed foliage smells very good. Its a nice tree to work on. Its very similar to both Lawson's Cypress and Leylandii Cypress from a distance.
The story is that due to its genetic height (but lack of structural girth) this tree gets too tall and always ends up leaning sideways. Then its branches hang down like a curtain.
Supposedly in England there is one at an arboretum that does this and they nick-named it "The car wash".