A call to freeze the nuclear arms race won widespread voter support yesterday in the closest thing to a national issues referendum the United States has conducted. A tough California gun control measure was losing overwhelmingly.

The nonbinding freeze resolution calling for U.S.-Soviet negotiations passed easily in the District of Columbia, New Jersey, North Dakota and Rhode Island, and was leading in Massachusetts, Montana and Oregon.

However, the freeze vote was close in California and Michigan and losing in Arizona. It was leading in 24 scattered local jurisdictions, including Dade County, Fla.; Cook County, Ill.; Suffolk County, N.Y.; Philadelphia and New Haven; and was behind in only two Arkansas counties.

Late campaigning by President Reagan appeared to have weakened support for the measure in Arizona and narrowed the gap in California and among Republicans nationwide. "This is a clear national mandate," said Randall Kehler, national coordinator of the Nuclear Weapons Freeze Campaign. "I can't believe any elected representatives at the national level would be able to ignore it."

A CBS survey estimated that 55 percent of the members of the new House would favor a freeze resolution.

The propositions, whose language is similar on all of the ballots, direct governors and mayors to urge Reagan and Soviet leaders to begin negotiations aimed at a mutual and verifiable halt in production and deployment of nuclear weapons.

The freeze proposals were the most widespread of a record number of ballot initiatives, which sought voter verdicts on nearly 60 issues in 24 states.

Although the freeze movement faced little organized opposition early in the campaign, resistance came later from the Reagan administration and assorted conservative groups. Reagan spoke against a freeze and sent Defense Secretary Caspar W. Weinberger and State Department arms control specialists on the speaking trail to provide anti-freeze arguments.

Even though the initiatives would not be binding on the government, opponents argued that approval of the freeze vote would weaken the bargaining position of U.S. negotiators in talks with the Soviets and that a freeze would leave the United States in an inferior defensive position.

By far the most vicious battle involving ballot propositions was on California's tough gun-control initiative, which was losing 2-to-1. The proposal, viewed as a possible model for anti-handgun activists in other states, called for mandatory registration of all existing handguns by next April and an immediate ban on new sales.

Led by the National Rifle Association, opponents spent an estimated $5 million for a broadcast and newspaper blitz in an effort to stop the movement in a state that is frequently a bellwether of national political trends. Opponents outspent the initiative's backers by 5 to 1.

Such spending and a strong grass-roots organization that attracted help from hunters, retired military personnel and conservatives opposed to government regulation combined to whittle an early 2-to-1 lead favoring the measure.

Meanwhile, proposed constitutional amendments reaffirming citizens' rights to keep and bear arms were winning easily in New Hampshire and expected to win in Nevada.

In the most significant of several crime-control measures, Massachusetts residents appeared to be favoring restoration of the death penalty by 2-to-1. Measures to tighten requirements for allowing release on bail were leading in Florida, Arizona and Colorado.

Nuclear power issues were hotly contested in four states. A Maine initiative to shut down an operating plant, Maine Yankee in Wiscasset, was losing by 5-to-4. The proposal, which lost in 1980, would also ban future nuclear plants in the state.

Massachusetts voters were agreeing 2-to-1 to go almost as far in a proposal to establish complex legislative hurdles and require a statewide referendum for any proposed nuclear plant or waste disposal site.

In Colorado, a proposal for a fund to convert the Rocky Flats nuclear weapons plant to peaceful uses was losing, while Idaho citizens were favoring a measure to support the nuclear industry by requiring voter approval for any curb on nuclear power.

Cockroaches starred in a Massachusetts media battle over whether to keep a law requiring a five-cent returnable deposit on all beverage containers. Opponents broadcast commercials warning that the bugs would proliferate in stockpiled bottles, but the measure appeared to be winning.

However, the so-called "bottle bills" were losing badly everywhere else: in Arizona, California, Colorado and Washington state. Nine states have such laws on their books.

Five states considered questions relating to legalized gambling. Expansion of gambling was losing in Montana and South Dakota, while North Dakota was rejecting new restrictions on existing gambling laws. Colorado appeared ready to expand its operation, and Minnesota appeared to have legalized horse-race betting.

Taxes, a major issue in the 1980 campaign, were more controversial this year on local ballots than at the state level. In Oregon, a tax limitation proposal similar to California's Proposition 13 was deadlocked in fragmentary returns. Less-sweeping tax changes were on the ballots in Idaho, Maine, Montana, Nevada and Washington.

Missouri voters were expected to veto a new 4-cent gasoline tax for road improvements but to approve a 1-cent sales tax increase for more school funds.

Four states considered new utility regulations. In Michigan, residents voted on new rate-setting techniques opposed by the utility industry and, in Ohio, on whether to make public utility commissioners run for election. Missouri and Nevada decided whether to set up consumer advocate offices.

Ohioans were voting 3 to 1 against a sales tax hike that would finance a 600-mile rail system to link the state's major cities with a 150-mph "bullet train." It was expected to fail, largely because voters feared that inflation would drive the cost of the system far beyond the present estimate of $9 billion.

In another test with significance beyond state borders, Alaskans voted on a proposal to ban use of state funds for abortion, except to save the mother's life.

Alaskans also were deciding whether to fund a previously approved initiative to move the state capital from Juneau to a moose-populated swamp near Willow, 70 miles northeast of Anchorage.

Meanwhile, District of Columbia voters decided to ask for statehood under a controversial proposed constitution, and Idaho voters decided 3-to-1 to let "denturists" who are not dentists install false teeth.

The position of the federal government as landowner was an issue on ballots in Arizona and Alaska. Alaskans had a chance to demand that the federal government turn over its vast land holdings to the state, while Arizonans were voting against the repeal of a similar, previously enacted law that has been ineffective.