After two unsuccessful tries for the mayor's office, Jackson R. Champion has established himself as the District of Columbia's champion candidate by running as the Republican nominee for two other offices simultaneously in the upcoming Nov. 7 election.

Champion won enough write-in votes in the Sept. 12 primary election to qualify himself as the GOP candidate for D.C. delegate in Congress and for an at-large seat on the D.C. City Council.

The ballot containing Champion's name twice was approved last week by the D.C. Board of Elections and Ethics.

If he wins both posts, Champion told a reporter recently, "I just have to cut myself in half, since I believe that I am capable of representing the District of Columbia" in both legislative bodies.

Winfred R. Mundle, general counsel of the electoral board, said it was his "gut reaction" that Champion could not be certified to hold two offices simultaneously even if he were elected.

However, his chances seem slim. The best-known of his four rivals in the delegate race is incumbent Democrat Walter E. Fauntroy, probably the city's best vote-getter. In the at-large council race, he also faces four opponents, including Statehood Party incumbent. Hilda Mason and Democratic nominee Betty Ann Kane.

Champion lost by lopsided votes as the Republican nominee for mayor against incumbent Walter E. Washington in 1974 and in this year's Republican primary against Arthur A. Fletcher, now the party's mayoral nominee.

"It's not sour grapes," Champion said, "but as I look at the two candidates for mayor, I believe I will support Marion Barry over Fletcher."

Champion, 55, who formerly operated a beauty supply business, has worked outside the city Republican organization. He said he has not asked for its help in the two campaigns.

"I feel that I am obligated to the Republican voters who asked me to run" by the write-in votes they cast in the primary election, Champion said in a telephone interview.

He said he supports strengthening city laws to provide more jobs and contracts to minorities.

Even in the write-in votes, Champion did not win first place for the two posts he is now seeking. Fletcher, the mayoral candidate, got the highest number of write-in votes for congressional delegate, and Jerry A. Moore Jr., an at-large member of the council, got the highest number for council chairman. Both declined to have their names put on the general election ballot, clearing the way for certifying Champion's candidacies.

Another well-known name in D.C., politices in past years, Charles I. Cassell, also will appear on the ballot as Statehood Party candidate for council chairman. Cassell is a former member of the school board.

Also placed on the ballot, as the Republican candidate for the council from Ward 1, was David Patten Russell. All other candidates' names had been announced earlier.