I have a client who is trying to figure out how to tag her books at Amazon.
There's a category for Police Procedural, of course. But what about when the Procedural part is done by an investigator -- and not a PI, but someone who works for a private firm that consults with the police and Homeland Security and other agencies around the world. So although the tone is light and similar to a cozy, the protag's a professional, very good at what she does, and entirely respectful of rules and boundaries. In a fresh twist in fiction, she defers to her boss and doesn't stake out on her own.
Do we have an acknowledged term for that? Investigator Procedural?
Categories are intended to help readers find other books they will like. Since I love Ed McBain's 87th Precinct novels, I might also like yours. That your protagonist is not official police is less important than the fact the main character has a legit reason to investigate. In other, words NOT a librarian or zookeeper or philatelist solving crimes in her spare time.
Procedurals are also more a methodical-solve-the-case style plot than they are "and suddenly her evil twin sister turns up" (although Erle Stanley Gardiner used that double device more than once.)
You can always just use "crime novel" too.
But if you're looking to find readers, nothing beats "if you like Ed McBain, you'll like this" and "if you wonder why property values in Cabot Cover haven't dropped to zero, this book is for you."
And of course, look for similar books and see what categories they're in. No use reinventing the wheel if someone has already gotten their hands grimy for you.