Criminal suspects can't sue crime victims for reporting crimes. If the complaining witness testified under oath, whether in court or in pre-trial declarations, and if it subsequently becomes obvious that the testimony was a knowing lie, then the CW might conceivably be charged with the crime of perjury. That doesn't usually happen though.
It would be much more reasonable to file a civil suit for slander, defamation of character, that sort of thing. Anyone can file a civil suit and the court would have to present good reason for refusing to take it to trial.
In contrast, perjury is a crime that must be tried in a criminal court, not a civil court. The decision to prosecute that crime is made by the district attorney, who has enormous discretion in deciding which cases to pursue. If he decides not to take this one you have no practical way to get around him unless Bill Gates will loan you his lawyers.
Furthermore, in a criminal trial the jury must rule unanimously in your favor before the defendant would be convicted. In a civil trial only a majority of the jurors need to be convinced that you're right. If it's merely 7-5, you win!
But bear in mind that the outcome of a civil suit is measured strictly in dollars. If you win, the jury will award you a settlement which they think is fair compensation for the harm you suffer. They cannot and will not put the defendant in jail or add her name to some sort of "public menace" watch list.
Which brings me to my final point. The best way to win a civil suit is to prove that the defendant's wrongful actions had a negative economic impact on your life. Your boss fired you, with no income you couldn't pay your mortgage so your house was foreclosed, that sort of thing.
All the records from the criminal trial will be available as evidence so you'd better make sure there's nothing in there that casts your own character and reputation in a bad light, and makes the defendant look like a poor sad lady who went through a terrible ordeal and simply made an honest mistake.
Juries can and do award "punitive damages" for suffering and inconvenience, but you need a really good attorney to win that case. You have to prove that the defendant caused you some sort of harm that isn't obvious from a quick review of your bank statements. The defendant will have her own lawyer who will have you examined by psychiatrists and social workers to determine just how badly you've been harmed. They'll put your wife and children on the witness stand. They'll have some sneaky photographer produce photos of you on a happy family picnic, playing Frisbee with your dog. Or worse yet they'll get people who don't like you to testify that you've always been a depressed loser whom no one wanted to associate with, so nothing was changed by the defendant's actions.
Your lawyer will do the same to the defendant. These cases get really ugly.
And very expensive. Unless the outcome is obvious, your attorney probably won't want to take your case on a contingency basis, merely taking a huge portion of the settlement money. He'll probably want to collect at least part of his fee and expenses up front.
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There's a case in the Washington Post of a man who has spent 25 years (IIRC) in prison for rape--his entire adult life since he was busted as a teenager. Courts are slowly going through this huge backlog of convictions, using modern DNA analysis to reexamine the evidence. In his case it was found that he was wrongly identified, and he was released. (This gets way more complicated; he was convicted of another rape for which there was no DNA evidence, and the governor had to decide that he should be exonerated of that one too. And the man who was guilty is already serving life in prison and refused to testify.)
What a horrible thing to happen, right? Wait a minute, think about the rape victim, who in this case did not lie. She really thought he was the attacker, since he looks somewhat similar to the real guy.
She feels so guilty for what she did to this poor fellow, she can hardly live with herself. Talk about going through hell
twice over the same thing.
