Let me get this straight here. From what I could figure out of the premise from the J-Wiki article on the 1980 cop show "Daigekito Mad Police '80" (The Fiercely Fighting Mad Police '80), a near future Tokyo was struggling under a huge rise in organized crime activity due to a super-organization called The Champagne Mafia which has been given nefarious international support in the form of weapons and ammunition. Basically, what was needed was an elite police squad just as ruthless as the bad guys. In fact, it was supposed to be so ruthless that it was dubbed the Mad Police with the catchphrase for the series being "A shot is fired every 10 seconds, a bad guy is killed every minute!".
When I was living in the Tokyo area, the top news story on TV one night was that a police officer had to fire off a shot at a criminal. I don't remember whether the culprit had been hit or not although I think he was captured, but there were all sorts of reports and bedlam in the media and the police headquarters for a few days afterwards. And that was in the 21st century, a time in which it is still extremely rare for anyone in Japan to carry a firearm outside of the police, the military and organized crime members. So I can imagine that decades ago, shows like "Daigekito Mad Police '80" must have been the purest form of escapist fare on the telly.
The over-the-top opening credits for this show absolutely upped the ante for the usual opening credits for a Japanese cops-and-robbers series. Along with the typical running and grim faces of determination to get their man, there were now tons of explosions, fireballs, flying cannon fodder and guns...lots of guns. It's like witnessing "The A-Team" and a tokusatsu show involving a special forces squad who had been trained by Sean Connery's Jim Malone character from "The Untouchables".
Almost a couple of weeks ago, I wrote about a later cop show called "Jungle"（ジャングル）and noted that there were two singers in the cast. Well, "Mad Police" was no different. It had its own songbird in the form of Mayumi Horikawa（堀川まゆみ）as a happy-to-be-shooting-from-a-car cop.
Of course, for opening credits like that, the producers needed a song just as epic. So You, as in jazz pianist/composer Yuji Ohno（大野雄二）, & Explosion Band came up with the right theme. Compared with the even more legendary theme from "Taiyo ni Hoero"（太陽にほえろ）, there is more hard-boiled jazz thrown into the funkiness. And the interesting thing is that when the horns first come a-blazin', they go down the scale instead of up, as if to hint that the viewers are about to get down into the nitty-gritty of the seamier underbelly of Tokyo life.
If the theme for "Mad Police" sounds familiar, it is perhaps because Ohno has borrowed some riffs from his masterpiece anison, the theme song for "Lupin The 3rd"（ルパン三世）. You & Explosion Band incidentally, also has another entry on the blog which is a fair bit more sedate.