As any good lawyer will say, "It depends."
It depends on the type of charge and how charges are filed.
For misdemeanors, the District Attorney's office usually has up to one year from date of incident to file charges. If charges are filed after one year from date of incident, your attorney must address that issue (give notice) at the arraignment (defendant's first appearance in court). The date of incident should be stated on the Complaint or the date of offense listed at the top of the citation. The date of filing of the Complaint should be stamped by the court clerk somewhere on the Complaint.
For felonies, the amount of time the DA's office has to file charges depends on the type of charge and any special rules regarding discovery of the crime. For most general felonies (possession/sale of drugs, auto theft, felony assaults), the DA's office has up to 3 years from date of incident to file charges. For murder charges, there is no deadline to file charges since it is punishable up to life in prison. For other felonies, the time starts running not from the date of incident, but from the date when the alleged crime was discovered or reported (molestation, certain fraud/embezzlement crimes). The rationale in the law for this variation is that for some crimes, there is a delay in reporting of many years (molestation) or financial crimes are discovered after the alleged act was committed.
In short, if a person is arrested, it may take quite a while to find out whether or not a criminal case is filed.
What Happens After Being Arrested
For a non-traffic case, the police officer (or Detective handling follow-up investigations) will write a police report summarizing the incident. That report will be forwarded to the District Attorney's Office for review to determine if the office will file criminal charges. If the DA's Office believes there is sufficient evidence to prove guilt beyond a reasonable doubt at a jury trial, the office will file criminal charges through a CRIMINAL COMPLAINT.
If the DA's Office believes that based on the police report, no crime was committed or there is insufficient evidence to prove guilt, then the DA's Office will TURN DOWN the case.
If the DA's Office believes that more information is required in order to determine if charges will be filed, the DA's Office can request supplemental investigation. The police will do more investigation and upon supplemental investigation reports submitted to the DA's office, the DA will decide to either file charges or turn down the case.