A new study by the Urban Institute disputes the Reagan administration's claims that it has fully preserved the so-called "social safety net" for America's neediest, especially the administration's argument that local governments compensate for federal cuts in social services to the poor.

When the administration cut federal grants for services to the poor in the early 1980s, many administration officials predicted that the "truly needy" would not suffer. They argued that local governments would handle the cuts by eliminating services to people marginally in need, while protecting services for those most in need.

But it didn't turn out that way, according to the study, which traced developments in four major metropolitan areas from 1981 to 1983. The cities are San Diego, Richmond, Boston and Detroit. The Urban Institute study is one of the few that has looked in detail at specific cities and how they responded to cuts in federal program outlays. The Urban Institute is a nonprofit social sciences think tank here.

The study examined what happened when federal funds were cut for services to three of "the most vulnerable" groups in society: abused and neglected children, the chronically mentally ill, and the low-income elderly.

Authors Martha R. Burt and Karen J. Pittman found that local governments not only failed in many cases to shift funds from elsewhere to make up for federal cuts, but even cut their own contributions for services to these three groups.

Nonprofit charities filled some "but not all" of the resultant gap, the study found. The result was a substantial reduction in net outlays for services to these groups in San Diego and Richmond, some reductions in Boston and maintenance of services only in Detroit, located in a state with a long tradition of generous social services. Consequently, instead of remaining protected by the "social safety net," some of the most needy and vulnerable people in the nation suffered, the authors concluded.

Looking at budgets and levels of services, the authors found that state governments in all four locations did, in some cases, try to shift money from elsewhere to protect programs for vulnerable people but, except in Detroit, this was not enough to overcome the impact of the federal cuts combined with reduced financial contributions from local government agencies.

"Michigan, the state in our sample with the worst economic circumstances and the least favorable revenue situation during the period under consideration, did the most to protect all three of the vulnerable populations of interest in this study," Burt and Pittman wrote in their report, "Testing the Social Safety Net."

In several cases, states tried to make up federal cuts. In San Diego, the state raised its contribution from 1981 to 1983 for adult social services and its agency for the aging, although it cut funds for mental health. In Detroit, the state raised its contribution for all three of these items. In Richmond, it cut adult social services but increased its contribution for mental health. In Boston, the state raised social services and child welfare, but cut mental health care.

But the local governments, under financial pressures themselves, made their own cuts in funds they had been supplying as part of overall program financing. San Diego made substantial cuts in its own contributions for everything but mental health. Detroit cut the agency for the aged while raising mental health slightly. Richmond cut all four programs for which statistics were available. Boston made some cuts, as well.

As a result, net federal-state-local spending on the programs for these needy populations decreased in most cases. In four of five San Diego programs, net outlays were reduced 13 percent to 24 percent. In Richmond, all five programs studied were cut a net of 14 percent to 65 percent. In Boston, net spending for mental health went down 23 percent and for the agency on the aging, 8 percent, but adult social services and child welfare each went up 7 percent net.

Only in Detroit did a different pattern emerge for those programs for which statistics were available: Mental health went up 4 percent, adult social services 8 percent, and funds for the agency on the aging dropped a net of only 1 percent. Statistics were not available on children's services.

The authors concluded that, instead of reducing services only for less needy people, as the administration seemed to believe would be the case, state and local governments failed to make sure that the "truly needy" were "uniformly protected."

"We conclude that the needy people in the three populations we studied have suffered as a result of federal changes and local response," the authors said.