The majority of the time you can free roam while you are on the case, though the only things you can do outside of your current investigation is solve street crimes.Search for film reels,hidden cars,landmarks and badges.
If you finish all of the cases at one desk, go to cases at the main menu. Choose which desk you finished the cases on and it should say Streets of L.A. Free Roam. Then like other peple said you can find reels, landmarks, and cars. You can also do Street Crimes.