If you have ever wondered why restaurants in this city, from the greasiest spoons to the most haute of cuisines, must display Heimlich maneuver posters, it is because a choking Mr. Koch was rescued by that technique at a Chinatown restaurant in the summer of 1981. The next thing you knew, he invited Dr. Henry J. Heimlich to City Hall’s Blue Room, allowing himself to be used as a guinea pig while the doctor demonstrated his maneuver for reporters. In short order, the posters became mandatory.
By this NYT article from 1981, the maneuvre was indeed performed on Koch that year, and he invited Dr. Heimlich to the Blue Room.
Although the NYT seems to insinuate some relationship between the maneuvre being performed on Koch and the law being passed, I imagine such a relationship may be difficult to establish, since Koch's motivation and his specific influence on passing the law may be difficult to reconstruct. Thus I would like to limit the question on the mere temporal succession on both events: Was such a law regarding mandatory posters passed shortly after the maneuvre was performed on Koch? The claim is absent in Koch's English Wikipedia article, but appears in its German version. I am skeptical about the claim, but hesitant to change the German article against the authority of the NYT.