What is a criminal "complaint"?
An arrest, by itself, doesn’t begin formal criminal proceedings. Rather, the filing of a document in court is required. In most instances in state court, the document of choice is a “complaint.”
Complaints can be either civil or criminal. Civil complaints initiate lawsuits, typically between private parties or a private party and the government. Criminal complaints, on the other hand, almost always involve the government alone. (Some states technically allow citizens to file criminal complaints, but the practice is quite rare.)
A state prosecution usually begins after a police officer arrests someone and presents the case to the prosecution. The latter then files a complaint, which charges the defendant with the relevant crime(s). So begins the legal process.
A complaint typically lists: the defendant, the date of the alleged offenses, the alleged offenses (including the relevant statutes, and whether the violations are misdemeanors or felonies), and some kind of description of the alleged facts underlying those offenses.
Here is an example of a criminal complaint.