The Supreme Court yesterday let stand a ruling barring North Carolina from publishing a "motorist's prayer" on its official state highway map.

The justice refused to hear the state's appeal of a lower-court decision that printing the prayer violated the Constitution's bar against state establishment of religious.

Each year the North Carolina Department of Transportation publishes and distributes free copies of the map. One side shows the highways and roads in the state; the other has scenic photographs, a message from the governor and the "motorist's prayer."

The prayer asks for "safe passage through all the perils of travel" and implores God to "steady our hand and quicken our eye that we may never take another's life; guide us to our destination safely, confident in the knowledge that thy blessings go with us through darkness and light . . . sunshine and shower . . . forever and ever. Amen."

In other action yesterday:

The justices agreed to review the legality of a pooling arrangement that Democrats say allowed Republicans to overspend federal limits in Senate campaigns in 1978. The case also involves the powers of judges to overrule the Federal Election Commission.

Under federal election law, a party's national committee may spend a certain amount for any Senate race and a party state committee may spend a certain amount. Some committees, especially where there is a safe Senate seat, are able to raise well beyond their needs for any campaign, however, while others can't even raise enough to come close to the federal spending limit.

The national Republican Senatorial Committee in 1978 discovered that by pooling all the money -- state and natrional -- it could then reallocate funds not needed to campaigns that were running short.

The Democratic Senatorial Campaign Committee sued to stop the practice, contending that this allowed some state Senate campaign committtees to spend far more than they would have been able to raise on their own.

The FEC rejected the Democratic complaint but the U.S. Court of Appeals in Washington ruled the Republican arrangement illegal.

Yesterday the court agreed to review the appeals court holding, which was also challenged by the FEC.

The court said it will decide whether workers with access to management's confidential files can join a labor union, a case which could affect secretaries and the thousands of other white-collar employes.

The justices said they will hear National Labor Relations Board agruments aimed at granting the right of union membership to most such workers.

The board is seeking to overturn a Seventh U.S. Circuit Court of Appeals ruling that barred anyone dealing with confidential front8office matters from union rolls in Illinois, Indiana and Wisconsin.

The court refused to block a judgment "in excess of $3 million" against the city of Chicago for discriminating against its female employes.

In an unsigned order, the high court rejected arguments by the city corporation counsel, Stanley Garber, that the city has a "bone fide" merit employment system, which is exempt from Title VII of the 1964 Civil Rights Act and the Equal Pay Act.

Federal courts in Chicago ruled earlier that the city paid female custodial employes in the Department of Public Works and clerks in the Department of Water and Sewers less than their male counterparts for the same work.

The lawsuit was initiated by the National Organization for Women in 1974 and charged discrimination in hiring, promotions and wages.

Although Chicago modified its employment practices in the early 1970s to conform to civil rights laws and adopted new job tests, the NOW suit charged, women still were dominant in the lower paying jobs.