In theory, you should be able to pick up a signal from thousands of miles away, if the broadcast has sufficient power. In reality, many frequencies are “Line of Sight” i.e. they don’t go over the horizon. This is especially true of police and fire in urban settings, where the signal may not need to travel the vast distances covered by very rural emergency services. As an average, and it will depend on the type of radio systems being used by your local police, expect about 25 to 50 miles of a signal picked up from your location.