I've included some dramas that have a big legal component and some crime, but I wouldn't consider them crime dramas. It's possible that there may have been a female character who likes the ML in some of these that was so minor I've forgotten about her.
Some of my favourites:
Healer (reporters / some action / a very small amount of politics)
Coffee Prince (gender bender)
Bromance (gender bender / some action)
I Hear Your Voice (Noona / law with some crime / fantasy element)
While You Were Sleeping (law with some crime / fantasy element)
Also good :
Go Ho's Starry Night (office)
Queen In Hyun's Man (time travel, so some historical bits but mostly in the present)
Witch's Romance (Noona / office)
It's Okay, That's Love (not a standard medical drama, but psychology / mental illnesses are a huge component)
Kill Me, Heal Me (also involves psychology / multiple personalities)
Bring It On, Ghost / Let's Fight Ghost (fantasy / you could technically call the fights action / crime I guess, but it's really not that serious)
Pinocchio (reporters / some crime / some revenge)
Not in my personal top 40, but worth checking out based on your criteria:
Heartstrings (music majors / there's a female rival but I can't remember if she had feelings for the ML or not)
