Most common law enforcement vehicles tend to be known for their speed capabilities. In space, anyone can go as fast as they want if they have enough fuel, since everything drifts in space. Thus, it would be important for law enforcement craft to be able to get up to speed faster than other ships. To do this, they either need more power propulsion systems, or to be physically lighter. Having a powerful propulsion system that has a low fuel requirement would be ideal, as propulsion would have to counteract the total mass of the ship, even in a vacuum. (Correct me if I'm wrong)
Design wise, ships could be in any ridiculous shape, since they do not need to worry about air or water friction. One could create a massive brick wall and it would still function in space. Minimizing on-board vibration because of the engines would also be important, so the ship doesn't shake itself apart. With graphyne or carbon nanotube technology, any space craft can remain lightweight yet well armored, and these two materials (especially carbon nanotubes) have a wide variety of technologies they can comprise, making these craft even lighter.
Next question then is: "Who are they chasing?" and "Will these craft need to enter atmosphere?"