Answer:
If someone names you as a criminal and you are then arrested, but the report was false, then you can sue the person who lied to the police. However, there typically have to be "damages", such as injuries, lost wages, loss of your reputation, for you to get anything from the lying person, and they have to have some money for you to win anything. It's best that you contact a lawyer in this situation to see what you can do about a false police report.