Looking for an old horror movie

When I was about 10 (17 years ago) I caught a movie on TV, which seemed to be one of those murder mysteries about a bunch of people in a mansion that get killed one by one. It was an old black and white movie, so I figure it's from no later than the 1960s. The only specific thing I remember from the movie is that they found a dead guy in a closet with his eyes open, and then in the next scene there were two women talking about it (I think they were laying in bed?), and one of them said something to the effect of "I never knew a person could die with their eyes open". That's all I remember.

I lost the movie before it ended because I, stupidly, pushed a button on my TV, I don't remember what I was trying to do, but suddenly the movie was gone and I was on some other channel. I tried and tried to find the channel it was on, but I never figured out what I did wrong and I never got it back. Which bummed me out because I had been really absorbed in the movie.

Anyone know the movie I'm talking about? I've always been curious to see it again.