Books with: Paranormal Romance where the female is a detective/ solves crime.

[Isabella]

Paranormal romance where the female might be a detective or just someone who solves murders.

[Lauren]

Maybe Blue Twilight by Maggie Shayne?

The heroine and private investigator is Max and the overall series is twilight hunger. The paranormal part is vampires

[Lynn]

What about....
Ghost Mortem
Abby Cooper, Psychic Eye
Magic Bites
?

[Anna]

Burn for Me

[Tori]

Charlie Davidson series?

[Stargazevaze]

The dark fae FBI series
By C.N Crawford
The first book is the agent of enchantment
https://www.goodreads.com/book/show/3...

[Cynthia]

Kate Danley Maggie for Hire
although I don't remember if there was any romance in it

[Judy]

Broken Witch Episode One
Rogue, Renegade And Rebel
Witch of the Federation
A Curious Invasion
The Last Necromancer
The Glass Gargoyle
The Strange Case of Finley Jayne
My Immortal Soul Book One
Angel: Private Eye #1
Hear No Evil

[Amy (Other Amy)]

Unholy Ghosts is one of my all time favorites, but it's a slow burn romance; she won't be getting her man in the first book. (She's not a detective, but she is solving murders.)

Rosemary and Rue trends more to urban fantasy than paranormal romance, but you might like it. (Again, you'll have to read the series to get the romance; the first book is just our detective being a large walking disaster.)

I read Once Bitten, Twice Shy quite a while ago, and I don't remember if they are solving murders in the first book. Definitely in the series somewhere though.