The Crimson Kimono (1959, Samuel Fuller)

Dancer Sugar Torch is surprised in her dressing room, then chased down and shot to death in the street. Enter the cops: Glenn Corbett (star of Homicidal) and James Shigeta (of the musical Flower Drum Song). Delightfully drunk artist Mac (Anna Lee of Hangmen Also Die) points Corbett to painter Christine (Victoria Shaw of Edge of Eternity), who knew about Sugar’s new act, The Crimson Kimono, a geisha thing.

Corbett and Mac:

Lots of twisty witness-questioning ensues, and it turns out the killer is a wigmaker who thought her husband was cheating with Sugar. More interesting is the rivalry stemming from both cops falling in love with Christine the painter, which explodes when Joe beats his partner senseless during an official police kendo match. She ends up with Shigeta, the interracial thing being a pretty big deal for 1959.

Shigeta and Christine: