Assuming it is, you may have an action against the accuser for Defamation of Character.
Defamation of Character exists when an individual either states or writes (and subsequently publishes) certain statements that defame (i.e., harm the reputation of an individual). Defamation of Character is broken down into Slander (which is spoken defamatory statements) or Libel (which is written defamatory statements).
Assuming the individual made certain statements about you to the police regarding this domestic violence situation, you may have an action against the accuser for Slander. To prove Slander, you must show that the person: 1) made certain false accusations about you, 2) the statements cause you harm (i.e., reputational or otherwise) and 3) the statements were made either negligently or with actual malice by the accuser.
Furthermore, some statements are called Defamatory Per Se. A Defamatory Per Se statement is a statement that is so harmful, that it is presumed to cause harm to the person's reputation. False statements that allege one committed a crime is a Defamatory Per Se statement. This means that, in order to be successful in your claim against the accuser, all you need to show is that the statements were false and that the accuser knew the statements to be false.
Do you have any follow up questions based on what I have provided thus far? If so, please ask and I would be happy to continue assisting.
If not, please remember to click ACCEPT and RATE my assistance positively as that is the only way experts here can be credited for assisting customers. Thanks!