Local government, the one that's closest to the people, is becoming a depressed industry in many large American cities as municipalities and their workers compete for dollars beset by double-digit inflation.

Both city and labor officials say that one sign of the decline is the increasing number of public employe strikes, such as the 11-day walkout -- the first in 14 years -- by 33,600 New York City transit workers that ended Friday night. They also predict troubled municipal labor relations for years to come.

Though reasons vary from place to place, money -- or the lack of it -- rapidly is becoming the dominant factor.

Many urban observers think that as cities and their workers fight to keep up with double-digit inflation, they are destroying one another in the process. u

"It's an absolutely awful situation," said Michael Grace, spokesman for the Public Employe Department of the AFL-CIO.

"Public employes don't want to strike, but many of them are fed up. They feel as though they're being used as the scapegoats for everybody's money problems," Grace said.

A recent fiscal survey of 100 large and moderate-sized cities conducted by the U. S. Conference of Mayors, a major Washington-based lobbying group for urban America, shows:

Three out of four are experiencing budget difficulties or anticipate serious fund shortages next fiscal year.

Eighteen of the cities, including Washington, plan large layoffs of public workers in an effort to reduce costs.

Tax and fee increases and major service reductions are under consideration by 29 cities in the survey.

Many municipal officials who have grown dependent on large injections of federal cash say their problems will worsen if Congress approves President Carter's proposal to eliminate the states' share of federal revenue-sharing money, which is $2.3 billion a year.

Local governments receive a direct revenue-sharing subsidy of $4.6 billion. But many have drawn heavily on the added federal money flowing through their state legislatures.

All of this bodes ill for municipal labor relations, according to Roger Dahl, a labor specialist who serves the mayors' conference as well as the National School Boards Association and the American Association of Schools.

"We're in for a pretty rough period that could last anywhere from two to seven years," Dahl said. "I believe we're going to see more public employe strikes . . .

"There's just so much frustration out there. Even if mayors and city councils agree that raises are needed for their workers, they aren't going to be able to find the money to pay them."

Strike studies by the American Federation of State, County, and Municipal Employes (AFSCME). the nation's largest union of public workers, support Dahl's contention that more labor discord is likely in the public sector.

Before 1965, the number of public-worker strikes was small, ranging from 20 to 40 annually, according to AFSCME researchers. Since 1969, there have been at least 325 public employe walkouts each year, the researchers said.

In 1975 there were 478 public-employe strikes; this fell to 378 in 1976, rose to 413 in 1977 and increased again to 481 in 1978, the year of latest figures.

"In the last few years, the issue has been money," said Don Wasserman, director of AFSCME's research department. He said "a very heavy number of the strikes" have been mounted by school teachers seeking better pay.

Layoffs and local government requests for "givebacks" -- sacrifices of benefits and salary gains won in previous contracts -- also are contributing to public labor unrest, labor officials say.

Cities in the Northeast and Midwest that have been struggling the longest with budget shortfalls caused by declining tax bases and inflation have been the most active in paring their labor forces through layoffs and "natural attrition" -- refusing to replace retiring workers.

For example, between October 1975 and October 1978, Cincinnati cut its workforce from 19,449 employes to 8,089. In the same period, New York City trimmed 45,080 workers, winding up in 1978 with 337,150 employes. Public workers here in Washington fared "better," losing 1,099 jobs (from 47,878 to 46,779) between 1975 and 1978.

Nationwide, the number of people working for city government fell slightly from 2.536 million in 1975 to 2.511 million in 1978. Manpower analysts in organized labor and in the federal government say that public-job losses in the Snow Belt were offset by gains in some prospering Sun Belt cities.

AFSCME's Wasserman contends the cutbacks in public employment and citizens' calls for tax cuts a la California's Proposition 13 are hurting the affected local governments as much as they are hurting the workers.

"What you have are governments trying to function with fewer and fewer people," Wasserman said. "Some people would have you believe that this is being done with an increase in efficiency. But in most of those cities, there is a real deterioration of services," he said, confirming information in the mayors' conference report.

Meanwhile, leaders of organized public employes puzzle over their delemma. On the one hand, the labor leaders' goals are to obtain, maintain, and improve pay and benefits for members. On the other, some privately concede, there is little real argument in many cases that the money isn't there.

The option to strike, taken in frustration by many organized public workers, also poses problems.

"Public employes are at a distinct disadvantage in any strike action," said Grace. "The elected officials they have to deal with are the people who command most of the media attention. There also is the constant question of inconveniencing the public, and the bad feelings and publicity that generates.

"Most of your public employes won't go on strike unless they believe it's for something serious," Grace said.

"Strikes are war and in a war, there are no winners or losers. There are just survivors," he said.