Seems that anywhere you have a double staircase, this myth pops up. Not long ago, I heard it said at Virginia’s Governor’s Mansion (at 201 years of age, the oldest occupied governor’s house in the fifty states), where there are two staircases in the center of the house, one opposite the other. In this instance, however, the docent correctly pointed out that the story was, indeed, a myth. In truth, the two staircases were meant to separate the slaves and servants from the family. Many large historic houses have two or more staircases; the nicer one, usually in the front hall, was meant for the family and guests, the smaller, narrower, and usually steeper one for servants.
Another sort of double staircase is the mirror image kind that is seen on very grand mansions and palaces, like France’s Fontainebleau, below. This was built in the early 1600s, long before the Victorian era when ankle gazing was frowned upon. Decorative double staircases like these were designed for aesthetic reasons, to impress. As, indeed, they do!
And here is another example: West Virginia’s Governors Mansion, built in 1925, at a time when hemlines reached the knee, and no one was concerned about naked ankles. Double staircases were never intended to separate men from women.
History Myths Debunked 
I heard that myth about these mirror image staircases separating men from women years and years ago, but it always sounded like a fabrication to me. Glad to know I was right to be skeptical. Just wanted to add that there actually were separate staircases used by American men or women but not both. I’ve only seen this in one place, though, the dormitories where Shakers lived. . In the Shaker sect, men and women were considered equals, but the genders lived separately, sometimes under the same roof. Shakers led lives of celibacy. The men’s and women’s sides of residential buildings were identical, but each of the genders had its own staircase, doors, halls and rooms, and different sides of their religious gathering spaces. Trying to remove temptation I suppose.
Excellent point. Thanks for the Shaker note. You’re absolutely right.