You can use whatever publicly available resources you want to find anything. And LEO’s have access to a lot of databases that the public do not: driver’s license, vehicle registrations, public utilities, etc. There are even special law enforcement only type nationwide databases that pull from things like public records, credit checks, etc that will give you lifetime of history on a person. Finding an address for someone is actually very very very easy for law enforcement except in cases where a person has just moved or isn’t keeping a stable address. Like TV shows though they often make things tougher in novels than they really are to keep up dramatic tension.
The only caveat for some of these databases for law enforcement is that you must be able to connect them to an investigation. For instance a police officer can’t just run a person’s driver’s license because they want to, they have to have a reason but that can be a very minimal reason. It only becomes illegal for law enforcement if they are doing it for no legit reason - a bunch of cops got in trouble in Florida recently for many of them running the driver’s license of a female cop of another agency who was reported to be highly attractive. Or doing personal background checks on people for non law enforcement reasons.