If you say that you lied to the police, there are no specific charges for that. It is not actually illegal to lie to the police. There might be charges of Obstructing Justice, or if you used the 9-1-1 service there might be costs for making a false call. But it is unlikely the police would charge you for a first offense.
If you say that you lied to a Judge or Justice of the Peace, that's possibly perjury. It is uncommon for people to be charged with perjury, but it could happen. What is more likely is that if you say you lied, and if there is any evidence that the assault happened, the prosecutor will just argue that if you could like once, you could lie again ... so the Judge should look at the evidence and believe the statement that matches the evidence.
You need to understand that the prosecutor and the judge have likely both dealt with this sort of situation before. They have seen situations where people try to take back an accusation, and then end up getting hurt even worse a second time. So they are often reluctant to let the charges drop just because the main witness wants them to drop.
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My answer here contains only general legal information and not legal advice. No solicitor/client relationship has been created by this communication.