In some instances, a person who has been arrested will be released because the prosecution decides to not pursue formal charges. This is called “no papering” a case.
This is how one criminal defense attorney explains it:
In filling out the police report, the officer will typically include the criminal offense he or she thinks is merited based on the facts of the incident that led to the arrest. The police paperwork is then sent over to the “papering” unit at either the U.S. Attorney’s Office or the Office of the Attorney General where it is reviewed by a prosecutor.
The prosecutor decides first whether or not to paper the case at all. In making this decision, the prosecutor will presumably look at a number of considerations, including the seriousness of the offense, the accused’s prior record, the legality of any search or seizure associated with the arrest, and/or the willingness of potential witnesses to cooperate in the prosecution.
The government will typically decide to “no paper” roughly 10% to 20% of the cases. These are the cases that are called out first on the day of the arraignment.