Petitions with 18,701 signatures seeking a vote that eventually could make the District of Columbia the nation's 51st state were filed yesterday with the D.C. Board of Elections and Ethics.

If at least 12,451 of the names prove to be those of registered District voters, a citywide election would be held on the issue Sept. 9.

Approval would trigger a four-step procedure leading ultimately to a decision by both houses of Congress on whether to admit the District to the union as a state. Only a simple majority vote in each chamber is needed.

The petitions were filed without public announcement a few minutes before 5 p.m., when the elections board office closed for the weekend.

The signatures were gathered by the Statehood Initiative Committee, an offshoot of the city's tiny Statehood Party, which was formed by the late City Council member Julius Hobson Sr. and others with its main goal expressed by the party's name.

If statehood was ultimately approved, the federal district that was established by the Constitution as the seat of government -- which now encompasses the entire District of Columbia -- would shrink to the area generally along the Mall and embracing the Capitol and White House grounds.

The rest of the District would become a self-governing state, the name of which would be decided during the process of admission to statehood. It would have two U.S. senators and one or more members of the House of Representatives as determined by its population. It would expect to have full taxing and budget powers now denied under the current limited home rule.

The proposal differs significantly from the constitutional amendment proposed by Congress in 1978 that would give the District full voting representation in the Senate and House, but would maintain the existing form of the city government and restrictions on its operations.

That proposal has received approval from the legislatures of only seven of the 38 states needed for constitutional ratification, and is faltering badly.

Del. Walter E. Fauntroy (D), the District's nonvoting member in the House of Representatives and a leader of the drive to ratify the voting amendment, said he would "welcome thorough public discussion" of statehood. Fauntroy said he doubted that a debate on statehood "will in any way detract from the full voting representation question."

Hilda Mason, an at-large member of the D.C. City Council who currently is the Statehood Party's only public office holder, said the requirement for a simple majority in Congress should make approval much easier.

The statehood initiative would be the second held under a two-year-old law that permits District voters to use the ballot to enact or repeal legislation. Earlier this week, the elections board certified the first such measure of gambling in the city, which will be on the ballot at the May 6 presidential primary election.

The statehood proposal, if it qualifies, would be put on the same ballot as the primary election for the six members of the City Council who are up for election this year.

The proposal, if approved, would lead first to the convening of a convention to prepare the constitution under which the new state would function, and -- among other things -- to select its name.

The members of the constitutional convention, 45 persons selected from throughout the city, would probably be chosen at an election in November 1981 when voters fill vacant seats on the school board.

Once the proposed constitution were drafted, it also would be put up for a citywide referendum. Then if that document were approved. It would be submitted to Congress with a request for the admission of the District to statehood. This was the procedure followed in admitting to the union the 49th and 50th states -- Alaska and Hawaii.

The measure to be put before the voters next September also provides for creating a statehood compact commission, which would study steps needed to transfer power and functions from the federal and existing District government to the new state.

Although the measure does not say so, presumably the state would have a legislature replacing the City Council and governor replacing the mayor.

For a time in the period after the Civil War, the District had a territorial legislature similar to that of a state. That structure was replaced by a three-member board of commissioners appointed by the president, which survived almost until limited home rule began in 1975.

The Statehood Initiative Committee has called a news conference for Monday morning to announce the filing of more than 20,000 signatures. The announcement is still scheduled, but the committee jumped the gun with yesterday's filing of the 18,701 names out of fear that snow expected over the weekend might disrupt plans.

Lou Aronica, the party's information chief, said enough additional petitions should be filed Monday to top 20,000 signatures.

Initiative measures gualify for the ballot if they are ruled to be legally proper and if the petitions contain valid signatures of at least 5 percent -- currently 12,451 -- of the city's registered voters.