She is a cross dresser who is married to Hollis Green but dresses like a man. They shamed her by forcing her wear the pink dress. Obviously Hollis Green likes it as she is his first, most important wife..but he does have other wives also. She behaves as a man in the show, although at certain times does show emotions of a woman.very strange character, though.

She is really interesting in Big Love. I love the Greens. I wish they would involve them in more storyline arcs which I'm hoping they will now for the rest of this season and then next. Hollis, Selma, and then the big Russian looking guy are just really interesting and really do seem evil.

The Greens are all total crazy nut job mobsters. Selma is usually in a full suit and tie, looking more like a man than her husband Hollis. I believe that Selma and Roman are actually brother and sister, or at least share a father. I don't think she is a lesbian, but she sure dresses tough most of the time. Comes with the job of being a co-leader in a criminal organization. I see on here that she has done plenty of acting for years, but this character is off the chart.

Season 3, Ep. 7, Fight or Flight - While in the barn with Hollis Green and Selma, Roman Grant refers to Selma as his younger sister and Hollis as his brother-in-law. And of course, she is dressed in a pink gown when they try to force Cathy to marry Hollis. Why she usually dresses as a man is anyone's guess.
Susan in VA

Yes, he referred to her as his "brother", but he also says that she is his wife. Just remember, there's a lot of inbreeding in this family. Who knows what's going on there.

No more Greens, they freak me out! It's good drama but it makes me wanna hide behind the couch.

She is Not Hollis's sister she is Roman Grants sister. As discribed in Wikipedia:
Selma Green, Hollis' first wife and partner, Roman's youngest sister. A woman, but usually dressed in a man's suit with a male hairstyle and a masculine-deep voice

But it is so strange that nobody in the show has mentioned it or even cracked a smile about the obvious gender confusion. If Selma were not a woman's name, and if we didn't know she is played by a woman, there might be no reason to think she's not a man on the show. I can only guess that they will offer an explanation at some point.

Thanks for the clarification. I had been wondering this myself and thought this was the situation.

Yes, I did notice that she was refered to as "brother". I thought it was her, and I was right.

and he referred to her as "my brother, Selma"it's just a wacky in-bred family

She is playing the lesbian sister of Hollis Green.

Well considering her name is Selma I'd assume she is supposed to be a woman.