I'm assuming the situation is that this female clone of me just appears with an exact copy of my thoughts opinions and memories, instead of having gone through her own life from birth to present day. In that situation we'd be identical genetically, but not mentally. Basically twins.
This is the way it plays out in my head. I think a clone would make a good companion, we'd make a good team and such but probably wouldn't be too good with conversation because we'd have the same opinions on everything. I don't think that'd be too much of a problem because we'd both know that, and we wouldn't and up upsetting one another over it.
On the subject of sex, I'm a big pervert deep down on the inside (I'm good at hiding it), so she would be too. We'd know all of each others fantasies and turn ons. Knowing me, that would probably lead to something sexual. HOWEVER, also knowing me and that I would never cheat on my girlfriend, we probably wouldn't do it. Unless my girlfriend is up for a threesome. Then it's ON.
This is all fantasy though. Honestly if something like that happened in real life I'd be a bit too freaked out. Obviously it's not possible to clone an immediate copy of yourself, so I probably wouldn't believe it. Wow, there's some girl who looks like me in my house. WTF? Even if I did believe it was real we'd probably just be friends, as I'm very shy and logic would dictate that sex would be incest rather than masturbation. That'd be way too weird, and there would have to be some sort of consequences to sleeping with a clone of myself. Not to mention, like I said before, I'd never cheat on my girlfriend. Even though she's me, I would still consider it cheating.
So the bottom line is, either way we would definitely be friends. As a fantasy, we might sleep together but in real life that'd be way too weird and definitely off limits. We'd be friends and nothing more, and she wouldn't interfere with my relationship with my girlfriend.