Christine That is an interesting question. I don't think so! If Olivia had a twin, she would not have been so naive as to mix up Sebastian and Viola. Twins know that game of switching places (although it is not really possible with a male and female.) Still, I get the idea that Olivia was not a twin herself.
Ed Belsan They were twins. See V.i.235. This, of course, plays into all the gender identity confusion and comedy.