A minefield of politically sensitive civil rights decisions confronts Patricia Roberts Harris as she takes power as the new secretary of health, education and welfare.

Many of the cases, ripening for years within the HEW office of civil rights and now ready for action, involve states that President Carter must win to gain reelection in 1980 - Texas, Maryland, Alabama and North Carolina - or traditionally Democratic cities like New York and Chicago.

If Harris moves along boldly, she could provoke public conflicts with several southern governors and powerful Democrats like Chicago Mayor Jane Byrne, conflicts that could become as bitter as the University of North Carolina dispute that helped sink former HEW secretary Joseph A. Califano Jr. and that could threaten Carter's reelection prospects.

On the other hand, if Harris acts in a way that civil rights advocates believe is too soft, she will undoubtedly be subject to sharp criticism from civil rights leaders, with the possibility that some blacks, who gave Carter so much support in his 1976 election as president, will turn against him.

Joseph L. Rauh, attorney for black plaintiffs in the North Carolina case and many of the other disputes that will soon begin to move to center stage, said yesterday, "Secretary Harris has some tough desegregation decisions to make the next few months. HEW's office of civil rights and the entire civil rights movement will be on one side. Some politically potent mayors and governos will be on the other. We hope we can count on the secretary to reject political considerations and lead the way to integrated educational opportunities."

The roster of forthcoming civil rights cases on which HEW must make some decision, under its power to withhold U.S. education funds from local governments it believes have civil rights violations, forms the background of the recent widely reported meeting between Harris and David Tatel, the hard-charging director of the office of civil rights.

Harris reportedly criticized Tatel for his presentation of the issue, made clear that she isn't jumping into any quick enforcement actions without thorough study, and reportedly stressed the necessity to move with "political sensitivity."

A spokesman for Harris said the issue was blown out of proportion and that she hasn't any intention of retreating on civil rights. But Rauh and others are now apprehensive.

One immediate problem Harris faces involves Chicago, where HEW recently notified the public schools that they are ineligible for $20 million in elementary and secondary school aid because of past covert segregation policies in the public schools.

Backing up this action is a 104-page report, in which HEW civil rights officials found that Chicago, in a series of actions going back to 1938, had deliberately but covertly kept schools racially segregated by zoning , school sitting and boundary-drawing decisions, by the use of mobile classrooms to keep black children at crowded black schools instead of shifting them to half-empty white schools, and by assigning black teachers to black schools.

Chicago has drawn up a plan to correct the effects of these alleged policies, and Harris must decide whether to accept it.

If she doesn't, it could end up in court action, busing orders and withholding of an additional $100 million or so from Chicago. Byrne showed up at Harris' swaring-in ceremony last week and was reported as saying she hoped negotiations will end the dispute.

Another problem, similar to the North Carolina case, involves investigations of alleged vestiges of segregation in higher education in eight states, Texas, Alabama, South Carolina, Delaware, West Virginia, Ohio, Missouri and Kentucky.

Not all these investigations are ready for decision or action, but in Texas, which Carter carried in 1976, a preliminary HEW report found evidence, according to the Texas papers, that the state hadn't made an adequate attempt to integrate the colleges, and some were still virtually all-white or all-black.

If Harris upholds the report and seeks to get Texas to adopt a desegregation plan on pain of losing hundreds of millions in federal education aid, it could lead to a political explosion bigger than in North Carolina, because the governor of Texas is a Republican with no political stake in helping Carter smooth things over.

In Maryland, many of the issues are the same: a system legally desegregated but with some colleges still largely all-white or all-black. A potential cutoff of at least $60 million is involved unless Harris and Gov. Harry Hughes agree on an action plan.

In North Carolina, the state and HEW have failed to agree on a program to overcome vestiges of segregation in the university system, a cutoff of $90 million is at issue, and Rauh has charged that any further concessions to the state would be total surrender.

In New York City, the office of civil rights has been investigating a charge by the NAACP that the city is violating civil rights provisions by plans to close four city hospitals in predominantly black areas to save money.