Does a citizen have to bring charges in a 415 PC or can the police make the charge?
The decision as to whether to file charges will lie with the prosecutor. A citizen may perform a citizen's arrest on a person and report the crime to the police, and the police may arrest and detain a person, but ultimately all evidence, police reports, etc. will be given to the appropriate prosecutor, who will have sole discretion to decide whether criminal charges will be filed.
Neither. The District Attorney or City Attorney is the one who is vested with discretion to bring or not bring charges.