We just had a thread about this.
I stand by my post in that thread. For it to be a cozy mystery, the crime solver absolutely can not be in law enforcement of any kind. There can be a secondary character who is in law enforcement, like a bumbling police chief etc. If a LEO solves the mystery, it’s not a cozy.
To me, Murder She Wrote set the stage for the popularity of cozy mysteries. Lifetime took it and ran a bunch of cozies based on book series.