Making false accusations against someone is not actually a crime so you could not press charges against the person for making false accusations against you.
Making false accusations against someone is known as defamation of character and there's now actual law against defamation of character and no charges can be pressed against someone for defamation of character and no one can get arrested for defamation either.
If someone is making false accusations against you then all you can do is take the person to court and sue the person for the defamation of character.
But there's no way of actually filing any legal charges against someone for making false accusations.
The best thing you can do if no harm is actually being done is to just forget about it and let it go.
That is unless the people continue to make false accusations against you and it's doing you or your job harm.