Not sure what you mean by press charges. If you are refering to criminal charges, you may not. Even cops do not press charges. DAs prosecute or press charges.
You might discuss the situation with a cop if the accuser's accusations were made under oath, perjury. You may also ask about false reports.
You may or may not have a civil claim which you an pursue. Speak to a local attorney about the viability of such a suit.
The above is not intended as legal advice. The response does not constitute the creation of an attorney client relationship as this forum does not provide for a confidential communication.
It is highly unlikely that you can press criminal charges. As for a civil case for defamation, it may be possible. However, you should understand that a complaint to a governmental agency such as DCF carries with it a qualified privilege to protect against litigation otherwise nobody would report anything. To prevail, you will need to show that the statement was made with knowledge that it was false for an ill motive to cause you harm. It is not enough that the statement was inaccurate if it was believed to be accurate.