TALES OF THE 77TH BENGAL LANCERS - 1956 - Phil Carey, Warren Stevens - opening theme - YouTube

Not a detective show, but one of my favorites. Phillip Carey later played Phillip Marlowe, so I guess this is detective show related.

This one was about two young officers in the 77thBengal Lancers in colonial India, and probably couldn't be filmed today. Political Correctness...