After Ramirez admits her role in Rachel's kidnapping in The Dark Knight, Dent flips the coin landing on the unscarred side and then knocks her out - she is then not mentioned again. What happened to her?
There is no reference to her again, but as you have yourself noted, the coin lands on the unscarred side, meaning Dent wouldn't have killed her. At least not directly.
Dent is bound by his preference for the determination of fate by fate, abandoning this would undermine the sanctimonious crusade he has embarked upon, and would also invite his own interpretation to events (and as such accept responsibility for his actions), which is entirely what he is seeking to evade.
Two face represents the duality of justice, that even in its execution it is able to occupy an 'unjust' position by virtue of of its extreme binary nature: 'Guilty' or 'Not Guilty'. His raison d'etre purpose is to become a conduit of the cosmic forces of fate, or in the terms he describes it ...'Luck'. By totally removing his own perspective from the decision, he is able to carry out sentences without remorse or apprehension.
He represents the ultimate parable about subscription to a higher cause, in this case the law. The Cosmic Nuremberg Defense.
When Maroni 'passes' this test, the driver doesn't, and Dent executes him, despite being in the same car (resulting in a crash). He hasn't killed Maroni, he has simply invited another element of 'luck' into the proceedings, another opportunity for Maroni to fail.
However, this is an interesting example of how the system (Dent, being the extreme representation of justice) is designed to force a verdict against those which it has an investment in to be guilty. People can interpret that statement as they may, but it at least demonstrates a system that can be corrupted for personal gain.
Whilst this is only speculation, I imagine Ramirez was forced to pay for her insubordination and corruption, but the fact she acted as an accessory under duress (her mother was in the hospital) its unlikely her sentencing would have been severe. Certainly expulsion from the Police, however.
Dent, of course, would argue that the coin landed on the clean side because she was acting under duress and wasn't guilty of death, as that is the celestial/cosmic/chaotic judgement, so given the context its unlikely he would have discarded this.