1. So we know there was something in her past about Big Dogs that made her afraid of them. We know Rawlins once faced a "Thing" (I suspect Black Dog but can't find it anywhere) and was saved by her father Jack Murphy. That and Rawlins is one of the few people to get away with calling her Karrie. It might've been the same incident.
2. Her husbands.
-First husband was when she was 17, he was a bad boy with a Harley. Gregory Taggart about a decade older dies at 42 in Blood Rites.
-She had to sneak out to go to prom which she would've been around 17 and possibly dating Harley guy.
-Mama Murphy doesn't approve of divorcing her *second* husband implying she agreed with the divorce of the first.
-So my Theory is that Taggart was abusive, leading to Murphy's Martial Arts obsessions and trust issues.
-Husband number 2.Rich. FBI guy. Got together cause they were on the job, which later makes Murphy more hesitant to do the same thing with Dresden. Though admittedly this is fresh from the backdrop of her little sister marrying said ex. turning him into brother in law.
As psychologically analysed by ID Harry and summed up by Butters as " Wow. Catholics" (I'm from a large extended Catholic family so I don't take offence. It happens.)
As for Murphy's career well we know most of it as it happens in story. First met Harry when she fought a Troll as a Beat Cop got bumped up/down when she refused not to consider supernatural as possibility, so by the time of Welcome to the Jungle she was taking lead for the tougher investigations. The only other relationship we know of is with Kincaid, which on an ethical level Man Toy with professional assassin is a bit ick for me. (Then again Harry and Lea might be the same and I have less problems with that)
I know its a bit academic at this point as we're unlikely to see her again anytime soon.
Am I missing anything vitally important?