The theme song was written and composed by Takashi Matsumoto and Eiichi Ohtaki（松本隆・大瀧詠一）. It's a wistful and slightly foreboding ballad which would probably describe the life of a down-at-luck private eye. Yakushimaru's singing gives it a bit more of an innocence, and the tinkly piano of Ohtaki's arrangements can be heard in the back there, although it's a little more reserved. In addition, the piano intro reminds me of one of Neil Sedaka's old hits, "Laughter in the Rain"(1974).
This is the trailer for the movie which was released in July 1983.