The police can charge you if there is sufficient evidence to support the other person’s word. The police must be able to prove beyond a reasonable doubt that you committed the crime in question. If there is no physical evidence or witnesses, it may be difficult for them to do so. However, if the other person can provide convincing testimony and/or documents that support their version of events, then the police may be able to build a case against you.
In some cases, the police may not even need direct evidence in order to file charges against you. For example, if they have circumstantial evidence such as phone records or emails that suggest you were involved in illegal activities, they may be able to use this as grounds for charging you.
Ultimately, whether or not the police can charge you depends on the facts of your case and the strength of any evidence presented by either party.