Yes, it depends if your police force uses digital or analog. You can pick up either, but you have to have the right gear. If you have an amateur radio club nearby, ask them. They will absolutely know and will be able to stwleer you towards the right gear.
Unfortunately, DIY isn't much of an option here. If you want to fool with radio, however, I strongly encourage you to find an old "boatanchor" to work on. Those are tubed communications receivers made from the late 1930s through the early 1960s. Parts and tubes are much cheaper than hi-fi stuff, they have superb build quality, and you'll be able to tune in shortwave, amateur broadcasts and much else. With all the tubes, they sure sound good, too. Look at units from Hallicrafters, National, Hammarlund, Drake, and Collins.