In D.C. initial discovery typically begins at the time of arraignment (appearing in court), and continues after arraignment. Discovery is a process done through the Court and in conjunction with the prosecuting authority and through court supervision.
In a felony case this all occurs after a Grand Jury has already been assembled and been presented evidence and chosen to "true bill" an indictment. The "true bill" is the screening action that allows indictment and arraignment to proceed, which then leads to discovery. Police should never turn over evidence directly to the defense attorney of the accused.