The easiest way to find some non-standard police procedurals is to look into the urban fantasy genre.
I do enjoy it, though it is not my favorite genre.
If you have explored the genre though you will know that they frequently uses investigations as a genre trope and you can often get some, if nothing else, interesting plots, even if the protagonist isn't a police officer they often need to figure out the mystery.
They're urban fantasy because they're fantasy novels that take place in the modern world; however, do not get them confused with Paranormal Romance which is a very similar genre which may or may not feature a peace officer in some form or another. While they have the same elements, their focus is less on mystery and more on the relationship/s.
When it comes to sci-fi police procedurals I enjoy:
9 Tail Fox
by John Courtenay Grimwood
The book follows sergeant Bobby Zha of the SFPD. One day he finds himself in a new body and attempts to find out who murdered him.
It is a good book all around. But it may not be for everyone. I would say that it borders on the urban fantasy fence.
The Rivers of London Series
By Ben Aaronovitch
These are very engaging, no small thanks to the protagonist. The series follows a young London cop as he discovers that he has a talent for magic and ends up in the special division which focuses on supernatural crimes.
The series begins with "Midnight Riot" here in the US. In the UK it is called "Rivers of London". Be aware that they are the same book!
Pashazade, Effendi and Felaheen
By John Courtenay Grimwood
This one is a mix of cyberpunk and alternative history, though it has a strong procedural narration throughout. You follow a former street criminal who becomes a police employee in the city of El Iskandryia.
I will be honest, these are very strange, albeit great books.
KOP, Ex-KOP and KOP-Killer
By Warren Hammond
Juno Mozamb is your typical bent copper stationed on a backwater planet in economic decline.
Definitely a fun series to follow.
The Caves of Steel, The Naked Sun and The Robots of Dawn
By Isaac Asimov
Classics, calling them anything else would be insulting. Elijah Baley is a homicide detective in the New York City Police Department, but this NYC is 3,000 years in the future, and the victim, R. Daneel Olivaw is a robot.
The Barbie Murders
By John Varley
A short story which gets right to the point. It follows Lt. Anna-Louise Bach and her partner Jorge Weil, police officers in New Dresden, a domed city on the Moon as they uncover a strange religious colony.
The Retrieval Artist series
By Kristine Kathryn Rusch
A detective in Armstrong Dome on Luna investigates crimes involving aliens - there's a lot of politics and treaties between the various alien cultures that cause confusion and lots of humans go into hiding after accidentally breaking an alien law.
It can be hard to get through, but you will enjoy it and be well rewarded for your efforts. At least I was.
I know that I started on the urban fantasy note, so if you would rather go with sci-fi that has an urban fantasy character to it ou could try:
- Lives of Tao by Wesley Chu
- Brillance by Marcus Sakey
- Newsflesh Trilogy by Mira Grant
- Daemon by Daniel Suarez
- Nexus by Ramez Naam