Washington voters will get a chance this fall to launch the District of Columbia toward becoming the nation's 51st and only totally urbanized state, and they will get a second chance to decide whether to legalize some forms of gambling in the nation's capital.

The D.C. Board of Elections yesterday certified both initiative measures and placed them on the Nov. 4 ballot -- adding new, controversial local dimensions to an election otherwise dominated by the presidential campaign.

If enacted, the statehood proposal would dramatically change the nature of government in the nation's capital. Not only would the District of Columbia -- or whatever the state is named -- have full voting representation in Congress. But it would also mean that the city would gain the budgetary autonomy long sought by local officials, including clear authority to tax the income of suburban communters who work in the city -- something barred by the Home Rule Charter.

November's public vote on statehood would be far from final. Congress would have two opportunities to accept or kill the proposal, and District voters themselves would have to vote a second time on the issue.

The statehood initiative will reach the ballot, as the result of petitions circulated last winter by the Statehood Initiative Committee, all of them members of the city's 1,400-member Statehood Party.The elections board ruled that the petitions contained 17,281 valid signatures, 4,490 more than necessary to reach the ballot.

The gambling initiative is a modified version of a measure resoundingly defeated by voters in the May 6 primary election.

The new measure would legalize only a city-run lottery and numbers game, like those in Maryland, along with bingo games and raffles conducted for charitable purposes. It leaves out two of the more controversial proposals of the earlier measure -- pari-mutuel wagering on dog racing and jai alai.

The gambling measure also will reach the ballot as a result of public petitions. They were circulated by the D.C. Committee on Legalized Gambling, whose chairman, Brant J. Coopersmith, headed an official study commission that in 1978 recommended gambling as a source of local government revenue.

Coopersmith estimated yesterday that the now-proposed forms of gambling would yield $25 million to $30 million annually to the city treasury.

The elections board ruled that the gambling petitions contained 13,822 valid signatures, a scant 1,141 more than needed to qualify for the ballot. Petitions must be signed by at least 5 percent of the city's registered voters, and must be widely distributed across the city.

Two Baptist ministers who spearheaded opposition to the gambling issue in the May ballot, the Revs. Andrew Fowler and John D. Bussey, spent more than an hour yesterday questioning and disputing the statistical method that was used to determine the number of valid petition signatures.

In the end, the board voted 2-to-0 to accept the advice of its general counsel, William H. Lewis, and certify the measure. The votes were cast by Viginia P. Moye, the acting chairman, and Jeannine Clark, a new appointee of Mayor Marion Barry attending her first meeting. Chairman Albert J.Beverridge III was absent.

The statehood measure was certified by an identical vote.

The statehood proposal, if it survives a five-step governmental process starting with the November election, would give the District the same standing governmentally as, for example, Maryland and Virginia. The District would have two U.S. senators and one or two members of the House of Representatives, depending upon population.

The proposal is different from the D.C. voting rights amendment to the U.S. Constitution that was approved by Congress in 1978 and has been ratified for only nine of the necessary 38 states. That amendment would grant voting representation in both houses of Congress but make no changes in the city government itself.

Unlike the consitutional amendment procedure, Congress has the power by a simple majority vote to admit new states to the union.

Even if the statehood proposal is approved by voters in November, Congress would have the right to review -- and to veto -- the measure just as it has with bills enacted by the D.C. City Council.