Advocates for statehood for the District of Columbia completed their drive yesterday for a referendum on the issue next Sept. 9 by filing petitions with an unofficial total of 21,928 signatures.

To qualify for the ballot, at least 12,451 of those signatures must be found to be those of registered city voters. The election would be held at the same time as a primary for members of the City Council.

The Statehood Initiative Committee filed petitions Friday with the D.C. Board of Elections and Ethics containing 18,701 signatures.

Yesterday the committee met a legal deadline for its campaign with two more filings that pushed the total to more than 21,000, according to Ed Gunan, the committee chairman.Delores M. Woods, assistant elections adminstrator, said an official count would be made later.

Under D.C. law those seeking to put issues on the ballot have 180 days to collect signatures after the petitions are officially approved. Yesterday was the end of that period for the statehood advocates.

If the initiative qualifies, D.C. voters would be asked whether a convention would take over most of the territory of the present District. Once drafted, the proposed state constitution would be presented to Congress, which could admit the District of Columbia to the Union by a simple majority vote.

Statehood would give the District full local government powers and representation in both chambers of Congress.

By contrast, the currently proposed constitutional amendment would grant full voting rights in Congress but would make no change in the local government. The Voting Rights Amendment, officially proposed by Congress in 1978, has received approval from only seven of a necessary 38 state legislatures and is faltering badly.