If someone tells the police that they don't want to press charges can the person change their mind?

The person can change their mind but that doesn't mean the prosecutor has to dismiss the charges. The local prosecutor can continue with the case and if you don't cooperate you can be held in contempt of court and probably jailed. 

Steve Lombardi
Iowa personal injury, workers' compensation, motorcycle, quadriplegic, paraplegic, brain injury, death