The Criterion DVD has an interesting extra in which you can watch the screen tests for about five of the actresses who were vieing for the role of the Second Mrs. DeWinter, identified as "I".
You can also read, subsequently, Producer David O. Selznick's and Director Alfred Hitchcock's comments on the various actresses.
Vivien Leigh auditioned and she was so not right for the role, but she got to screen test with Olivier, so you get the bonus of seeing how Olivier's performance changed from this preproduction reading to the actual film.
Anne Baxter and Joan Fontaine, (Scarlet Johanssen is such a ringer for her that it is almost distracting,) are cleary the best in the readings, and it did come down to those two. Baxter was only 16 or 17 at the time, but she really nailed the overwhelmed nature of the character, I think she was Hitch's and Selznick's favorite, but Fontaine actually got the role. (That's Fontaine to the left with Olivier.)
Don't worry about Baxter though, she went on to star in Orson Welles' The Magnificent Amberson and acheived screen immortality with role as Eve Harrington in All About Eve.
Another bonus to watching the screentests is seeing how the scene changed from the test to the shooting. The screenplay was by playwright Robert E. Sherwood and it shows a little. The screentest scene is a little prolonged with dialogue and plays out with the beats of a stage drama. In the finished film some of this dialogue is trimmed down. And the direction of the scene is changed slightly.
Hitchcock was fond of saying that in film the dialogue is not as important as on the stage. For instance, in the scene to pictured to the left you can see, (even just by the still,) that what the characters are saying is almost superfluous. He was asked once if he had considered directing for the stage and he said that on the stage the writer is the authority but in film the director is the authority.