The shadow of a federal investigation into organized crime is hovering over the Nevada gubernatorial election.

With less than three weeks to go before the Sept. 12 primary, most of the political attention has focused on $60,000 in contributions that were solicited and then returned by the two leading candidates, Democratic Lt. Gov. Bob Rose and Republican Attorney General Robert List.

A federal grand jury indictment in Detroit and an FBI affidavit filed in federal court here alleged that powerful underworld interests partially own the Aladdin Hotel and the Arg ent Corp., which operates the Stardust and Fremont Hotels in Las Vegas. Hidden interests in any casino are prohibited by Nevada law.

List, who solicited contributions from Argent and Aladdin last spring, gave back the $15,000 given him by Argent and the $10,000 contributed by Aladdin immediately after the federal investigation was announced in July. Rose gave back the $25,000 he had sought and received from Argent 10 days later, but waited for more than a month, and the Detroit indictment, before returning the Aladdin money.

Rose's slowness in returning the Aladdin contribution has become a pivotal point in the attack of the principal Democratic opponent, fellow Las Vegas attorney John P. Foley, who campaigns as "the only candidate with no strings attached."

Foley, whose billboards feature the picture of a gigantic American flag, is an underfunded late starter whose television commercials are of poor technical quality. He is sharing the anti-Rose vote with state Sen. John Schofield, who is said to have considerable following the state's sparesely settled rural counties.

Both Foley, a Roman Catholic, and Schofield, a Mormon, draw votes from the same well the so-called "family voter," which in Nevada is apt to mean someone who does not gamble but who accepts the necessity of the gambling industry for business purposes and wants any underworld influence kept out.

Schofield and Foley also will share the vote of those opposing the Equal Rights Amendement, which will be on the ballot in November as an advisory measure. Rose broke a tie vote in the state Senate in favor of the Equal Rights Amendment, but the measure subsequently was killed in the state's lower house.

List favors the ERA, although he has sued the National Organization for Women for trying to institute a boycott of the state.

But the equal rights issue has been in the background of the Nevada campaign, which has focused on "gaming," as Nevadans invariably call their gambling industry. Rose fanned the fuel of this issue by casting doubts on the state's 1977 low regulating "foreign gaming."

This sweeping legislation, opposed by the casinos but favored by most Nevadans, gave the Nevada Gaming Commission authority to prevent casinos from setting up branch officesin New Jersey or other states that legalize gambling.

Casino operations will be allowed in other states under the law only if the other states meet Nevada's strict standards of gambling control and only if all the ownership interests are acceptable to Nevada.

This kind of regulation is necessary, say Democrat Foley and Republican List, to prevent criminal elements from moving in on legalized gambling. Rose says that "gaming licenses have the right under our free-enterprise system to seek investment opportunity whereever it exists, without unnecessary regulation by any government."

Rose's stand won the approval of casino owners, but it was denounced last week in a front-page editorial in The Las Vegas Sun, which said the lieutenant governor "is serving the interests of a few large hotels in Nevada (campaign contributors, no doub