The civilization has discovered an semi-unspecified type of FTL drive and spread among stars, but only a small portion of the stars in the galaxy is explored, settled and administered. Beyond the edge of administered space, there are some settled systems, beyond them are some more which are only explored or being explored, but the vast majority of the galaxy remains unexplored and this is changing very slowly.
How can the law enforcement catch the criminals who could simply run away from the administered space?
Let me clarify the available technology.
Faster than light travel is achieved via unspecified means and it expends fuel proportional to the distance traveled. While using the FTL drive, the ship keeps existing in the "normal space" and continuously changes its position (i.e. not wormhole). The ship is not restricted to preexisting pathways (i.e. not hyperdrive), except for the need to avoid obstacles, which are rare, localized and mostly near the stars, because the space is realistically empty (i.e. no "anomalies" and dangerous nebulae, just a boring universe as we know it).
There exists a preferred reference frame, relative to which the FTL travel happens and there is no violation of causality.
Travel time between two systems is reasonable. For smaller ships, it is comparable to the travel time between two larger cities by a car in the beginning of the 21st century. Range without refueling is similarly comparable.
The FTL drive is surprisingly easy to manufacture. In fact, so easy to manufacture that many ordinary people have a small cozy FTL-capable starship, equivalent to contemporary cars, but slightly bigger, allowing people to live in them.
Other standard tech onboard
Even the smaller car-like starships obviously have life support. They also have rudimentary matter synthesizer/recycler, allowing indefinite replication of simpler foods and smaller 3D-printed structures, as long as the needed matter and power is available. Ships have airlocks and EV suits in case you want to take a (space)walk. Finally, they are able to suck surrounding fluids, which can be used as fuel and/or building material for matter synthesizer/recycler. To refuel, collecting hydrogen will do, and this can be trivially done in the most of the systems.
No alien civilizations are discovered in the galaxy. The life seems to be incredibly rare, only few planets with unicellular life are discovered and maybe one or two with multcellular life, but none with anything even remotely resembling the central nervous system.