This was the slogan promoted by the city's Department of Environmental Protection in response to the drought-like conditions of the 1980s.
The signs still exist. The "Save Water" message is even on my city paychecks. "Save Water. Don't Be a Water Rat" is a sign in some city buildings.
5 December 1980, New York Times, "Advertising" by Philip H. Dougherty, pg. D13:
Marschalk, which did the recent public service advertising announcing the state's gun-control law, has now answered the call from the City Department of Environmental Protection to do something about the water shortage crisis. The agency believes the key to conservation lies with the young - they can bug the grown-ups into saving. So today Marschalk will film a commercial showing Mayor Koch explaining to 30 children how he is making each of them a deputy mayor for water conservation enforcement. (Shades of the Junior G-Man.)
The campaign theme will be: "Keep New York wet. Save water."
15 January 1981, New York Times, pg. A1:
Koch to Declare "Drought Emergency" Next Week
6 December 1982, New York Times, "City Planning New Ad Drive To Save Water" by David W. Dunlap, pg. B10:
In December 1980, Mayor Koch named every child in the city a deputy mayor in charge of saving water. Flanked by 44 of his deputy mayors in one television commercial, Mr. Koch offered tips on saving water and concluded, in chorus with the children, "Keep New York wet."
23 August 1985, New York Times, pg. D18 ad:
New drought regulations require that by September 1st "Save Water" signs must be prominently displayed in every building except one, two, three or four family homes. The signs must be at least 6 inches high by 9 inches wide. The sign must include the following language:
Report leaks and water waste
Call (212) 966-7500
(From the Department of Environmental Protection - ed.)