From IMDB:

The Portland Police Bureau’s Elite Special Crimes Unit is led by Det. Lt. Everett Backstrom, an alcoholic and smoker who is in failing health, but takes on cases in special circumstances.

From Netflix you can stream 13 episodes of season one.

Rainn Wilson (who played Dwight Schrute in “The Office”) plays Everett Backstrom as a cynical, alcoholic, smoking, bad food (if at all) eater, who must report regularly to a doctor whose reports either keep Backstrom employed or gets him dropped from police work. Repeatedly in the series he thinks out loud beginning with “I’m X (fill in a suspect) and I operate as follows (fill in case facts) …” He is a disappointed heterosexual who shares a dump of an apartment with a gay roommate who won’t accept Backstrom’s nonsense and often tries to help him. Everett Backstrom always looks like the wrath of God.

Backstrom has the help of Nicole Gravely (played by Genevieve Angelson) whose job is really to make Backstrom’s clever case solutions look as if he operated legally.

You may remember Dennis Haysbert as President David Palmer in the TV series “24”. Here he plays a manager in the police unit.

Because the plots and solutions and methods are original, this is as good a detective TV series as most.