This question is really best directed to criminal defense attorneys and really is not a civil rights question. Generally the police department turns over its investigative materials, including witness statements, to the District Attorney's Office, which is the office determining whether to prosecute and then potentially prosecuting an individual. If an individual is charged with a crime, that individual's criminal defense attorney will make a request for the discovery, and then will usually get all of the investigative materials. There may be some unusual instances when witness statements are not provided, however, that should be discussed with a criminal defense attorne.
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If a person is charged with a crime, generally that person's lawyer generally receives all the discovery in the case. There are some limited exceptions which vary from jurisdiction to jurisdiction. The best thing to do is to make sure you communicate with a competent criminal defense attorney and insist that he or she makes every appropriate motion/request for discovery. Refusing to turn over discovery relevant tothe charge, a defense, or a sentencing issue may be sanctionable by the court on a motion by the defense.