Many District of Columbia residents are puzzled, disappointed and frustrated by the city government's clumsy handling of routine water billings, and some neighborhood leaders believe Mayor Walter E. Washington is losing political support because of it.

Inside the mayor's closest circle of advisers, there are some who also believe that his handling of the water bill situation has significantly damaged the mayor's political image and could stymie has chances for re-election, should he decided to seek another term in 1978.

Nearly a dozen civic and citizen association heads were interviewed last week about the water bill problem. Many said that people in their neighborhoods view the water bill problem as an indication of inefficiency in city government.

Some blame the City Council for the continulaly troublesome water bill system, but most of those interviewed placed the blame on the mayor.

"The blame the mayor. Obviously, if he runs again, I don't think he'll get many votes, simply because of the water bills," said Thomas C. Cryant Sr., president of the Capitol View Civic Association in Far Northeast Washington. Bryant said many of those from whom he has heard complaints are senior citizens who supported the mayor in 1974.

"I worked for him in his first election campaign. We thought, wow, it's all going to change, but I'm not going to do it again," said Carol Currie Gidley, a 35-year-old advisory neighborhood commissioner in the American University Park area of the city.

"People are disappointed that they mayor is not the forceful, aggressive, compassionate leader that he should be," she said. "A more compassionate bureaucrat at the other end of the (water bill) envelope would have helped to explain and could have anticipated the kind of concern there would be from the citizens on the other end who had to open that envelope."

The mayor feels that he and Environmental Services Director Herbert L. Tucker are "making progress" toward resolving the perennially awkward water billing problem, press secretary Sam Eastman said last week. "He's never satisfied that we can't improve," Eastman said.

The spokesman said he did not know what effect the water bill crisis has had on the mayor's political standing.

"It's the way they went about it. We can't find any basis for how they're trying to do it," said Ann M. King, president of the Ft. Stanton Civic Association in Southeast Washington. "People feel there's something not quite efficient or else they don't know what they're doing or they're doing something haphazardly."

What appears to have most upset city residents in many areas was a lack of advance notice of what to expect. Many had received their last previous bills nearly a year ago, and it was only in that bill that an announcement of the rate increase was made.

When the new bills came, in addition to a statement of the new rates, there was only an accompanying card saying, "The enclosed water and sewer service bill is for a consumption period which is greater than the normal six-month period. This longer period is necessary in order to return the billing system to the regular schedule and also to bring your account up to date . . . We regret any inconvenience caused by this longer bill."

Edward Scott, chief of the revenue division of the Department of Environmental Services, acknowledged last week that there was only limited publicity of the impact of the new billing procedures.

"I don't think anybody but those of us down here who ran the figures through realized that the 40 per cent rate increase would do," Scott said. "For someone whose last bill (covering six months) was about $19, the new one was likely to be about $50," Scott said.

In some areas of the city, the apparent surprise with which the unusually high bills came was reminiscent of a confusing city change requiring reregistration of handguns and an unpopular and stunning increase in the price of auto tags (which was part of the same revenue bill that boosted the water rates).

The water bill increase also came on the heels of raises by as much as 60 per cent in the assessed value of some homes in the city and increases in other fees. That, coupled with proposed cuts in trash collection and street lighting, has caused some community residents to wonder where their tax dollars are going.