Today, in BATMAN #24, Batman does something he hasn't done since Earth 2. He proposes. And not just to anyone, but one of his primary rogues gallery members: Catwoman!
Sure, Catwoman isn't one of his psychotic, Arkham escapees, and yes, she's actually been a Justice League of America member, but she's still technically one of the "less than legal" characters. But then, as Batman is destined to say, "We're all criminals. We've always been criminals."
However, the question doesn't arise from Batman's choice in matrimonial partners, but in Bruce Wayne's. You see, Selina Kyle has a criminal record. She killed a lot of people, too, according to the I AM SUICIDE arc in BATMAN. Basically, she's known to be Catwoman.