Looking for the title of 2 detective tv series

They are early 2000 - 2010 so not new ones.

1. There is a female detective who solves crimes. She always has to rummage through her purse to find her police id. She is very good but quirky. There is one superior that knows her and wants to move her up the ranks but she doesn't want to. She was on the fast track once working abroad and something happened there.  that is all i remember 

2. There is a forensic investigator with the police but he gets bullied by the detectives. i think mostly because they don't understand his way of working because he is very smart.

Does anyone remember any of them?

The look is kind of similar but she is the main protagonist.

Fukuie Keibuho no Aisatsu 

2. trace or it could be smoking guns or unnatural or Zero no Shinjitsu