The Supreme Court ruled 7 to 1 yesterday that a state of local government doesn't violate the constitutional rights of its unionized employees by refusing to allow their union to file grievances in their behalf.

The court disposed of the case, which involved the Arkansas State Highway Department and Arkansas State Highway Employees, Local 1315, without hearing arguments and with an unsigned majority opinion reversing the 18th U.S. Circuit Court of Appeals.

The protections of the First Amendment include the rights of an individual to speak freely, associate with others and petition his government for redress of grievances, and the right of associations to engage in advocacy on behalf of their members, the high court said. But, its opinion added, "the First Amendment is not a substitute for the national labor relations laws."

Justice Thurgood Marshall began his dissenting opinion this way: "Now, this court is deciding vital constitutional questions withou even a plenary hearing."

If under previous decisions of the court "a public employer may not refust to entertain a grievance submitted by a union-salaried attorney, it is not immediately apparent why the employer in this case should be entitled to reject a grievance asserted by the union itself," Marshall wrote.

"I decline to join a summary reversal that so cavalierly disposes of substantial First Amendment issues," the justice added. Citing a conflict between the ruling of the 8th Circuit and one in 1972 by the 7th U.S. Circuit Court of Appeals, he said that "summary reversal seems to me an especially inappropriate way or resolving conflicts between the Circuit Courts of Appeals."

In the Arkansas case, two highway department employes such sent a letter to Local 1315 in which they stated a grievance and asked the union to process it. The local sent the letters to the department, noting that it represented the employes. The department did not respond. The employes then complained directly to a department official.

A U.S. District Court judge, upheld by the 8th Circuit, found that the department, in violation of the First Amendment, had denied the union the right to submit effective grievances on its members' behalf.

In the unsigned opinion, the Supreme Court held that the procedures used by the department "might well be unfair labor practices" under federal labor law.

But that doesn't establish a constitutional violation, the opinion said. The First Amendment doesn't "impose any affirmative obligation on the government to listen, to respond or, in this context, to recognize the association and bargain with it."

Justive Lewis F. Powell Jr. did not participate.

"FAMILIAR" LAWYERS' ABUSE

With only Justice William H. Rehnquist dissenting, the court allowed a tardy appeal of the conviction of a Philadelphia man whose court-appointed lawyer had deceived him, his family and his friend into believing that he had appealed, or would appeal, to the high court.

Represented by Rudolph S. Pallastrone, also of Philadelphia man whose court-appointed lawyer ahd deceived him, his family and his friend into believing that he had appealed, or would appeal, to the high court.

Represented by Rudolph S. Pallastrone, also of Philadelphia, Herbert G. Wilkins Sr. was convicted 2 1/2 years ago of kidnapping, interstate transportation of a female for immoral purposes, and conspiracy. The 3rd U.S. Circuit Court of Appeals rejected Wilkins' appeal.

Wilkins asked Pallastrone to seek Supreme Court review and, in September 1977, was assured by the lawyer that he had done so. But last July, a year after the filing deadline, Wilkins, by inquiring of the clerk of the court, learned that the petition hadn't been filed.

Wilkins wrote several letters Pallastrone, but the lawyer ignored him, just as he ignored inquiries from the Justice Department. Finally, last December, Wilkins filed a review petition from his cell at the federal penal facility in Lewisburg, Pa.

Supporting a charge that Pallastrone had "lied" and misled him with affidavits from his wife and minister, Wilkins said he was entitled to relief even though his petition was 17 months late. Solicitor General Wade H. McCree agreed.

Yesterday, in an unsigned opinion, the Supreme Court said it has a "strong interest in ensuring that lawyers appointed to aid indigents discharge their responsibilities fairly. Yet this prisoner's story of his appointed lawyer's indifference to his legitimate request for help is all too fimiliar."

The court sent the case back to the 3rd Circuit, directing it to re-enter its affirmance of conviction, but to see to it that Wilkins has counsel for a new appeal. Justice Powell did not participate. OTHER ACTIONS

The court refused to disturb a decision requiring Florida, as a condition of receiving multimillion-dollar grants under the Federal Rehabilitation Act, to tailor its rehabilitation program to requirements of the law and put regulations into effect.

The court left intact the Laetrile-smuggling conviction of Robert W. Bradford of San Jose, Calif., who as president of the 25,000-member Committee for Freedom of Choice, is a leading advocate of legalization of the substance for use in terminal cancer patient. He was fined $40,000.