The Supreme Court refused yesterday to review a death sentence imposed on a Texan whose electrocution could become the first to be televised.

But the court extended a stay of execution for Jerry L. Jurek so he can argue in U.S. District Court in Victogue in U.S. District Court in Victoria, Tex., that the state courts had violated his federal right by, among other things, letting him be represented by an "inept" lawyer later suspended from practice.

Jurek's new counsel also intends to argue that his right to privacy was violated by a Dallas federal judge's January ruling that executions of state prisoners can be telecast by a station acting as a "pool" for all electronic media.

After acting in the Jurek case, the high court heard an hour of argument in each of four unrelated capital punishment cases.

In one, the issue is whether the constitutional prohibition on cruel and unusual punishment is violated by a Georgia law permitting the death penalty for rape of an adult woman unaccompanied by further harm.

In another, the issue is the constitutionality of a Louisiana law making the death penalty mandatory for the intentional killing of a police officer performing his duties. Twenty-nine states, including Maryland, either have similar laws or laws making the slaying of a peace officer an aggravating factor that can be used in deciding to whether to impose the death penalty.

In the Georgia case, Ehrlich A. Coker escaped from a Waycross prison where he was serving sentences for two rapes and a murder. He entered a home, forced the 16-year-old wife, a recent mother, to tie up her husband and - wielding a four-inch steak knife taken from a dresser - raped her. A jury ordered him electrocuted. Georgia is the only remaining state permitting death for simple rape of an adult.

In behalf of Coker, who is white, David E. Kendall of the NAACP Legal Defense and Educational Fund emphasized that the death penalty for such rape was not provided by any of the 34 other states that have enacted capital punishment laws since 1972, when the court invalidated all of the old death-penalty laws.

In behalf of Georgia, Assistant Attorney General B. Dean Grindle Jr. argued that the discretionary death penalty is needed to prevent persons who commit rape or other violent crimes from repeating them.

Questions by Justices Harry A. discretionary death penalty for rape in indicated concern that nullifying the discretionary death penalty for rape in Georgia might lead to abolition of the death penalty in federal cases for such crimes as espionage and treason.

Kendall pointed out that several women's rights groups, in a friend-of-the-court brief prepared by the American Civil Liberties Union, opposed capital punishment for rape.

He said Georgia's brief contained "not one syllable in exculpation" for the history of the death penalty for rape in Georgia, which until the abortion of slavery considered it "a crime of property where the aggrieved was not the woman but her husband or father" and reserved the rape death penalty exclusively for blacks. "Even since 1861, the death sentence has rarely been imposed on white men," the ACLU said.

In the Louisiana case, the defendant. Harry Roberts, 19, was convinced of having fired a pistol through the open right front window of a marked New Orleans police car, killing one uniformed officer and wounding another.

The officers believed that Roberts fit the description of a 19-year-old black who had been firing a gun.

The injured officer wounded the assailant in the leg. Roberts, suffering from a leg wound, later was caught. At his trial, he took the stand to deny vehemently that he had been wounded by someone else.

For the state of Louisiana, prosecutor Louise Korns said there are no mitigating circumstances in slayings of this kind. Several law-enforcement organizations, in a friend-of-the-court brief, agreed, emphasizing that between 1966 and 1975 there had been 1,203 murders of officers.

For Roberts, Garland R. Rolling said - and Korns agreed - that the case was virtually identical to one in which a deputy sheriff had been murdered only 10 miles from the scene of the New Orleans police murder.

In that case, in what may have been an oversight, the Surpreme Court, without explanation, four months ago invalidated the mandatory death sentence. Then it ordered the validity of the same sentence argued in the Roberts case.