Mayor Marion Barry plans to send Congress the District's petition for statehood on Friday, city officials said yesterday, though its chances for passage any time soon are widely viewed as slim at best.

Delegates to the D.C. Statehood Constitutional Convention said at a news conference yesterday that they had finally completed the legislative history of the controversial statehood constitution, thus paving the way for the document to be submitted to Capitol Hill.

If Congress approved the constitution, the District would become New Columbia, the 51st state.

But congressional experts say that will not happen during this Congress, and they add that prospects for the next Congress, which begins in 1985, are not much better.

"If we brought it to a vote today, it would have a snowball's chance in July in Florida of passing," D.C. Del. Walter E. Fauntroy said earlier this year.

Fauntroy and other city officials have been critical of the constitution itself and believe it must be revised.

Among the more controversial elements of the constitution are a sweeping bill of rights that gives all government workers the right to strike, guarantees each citizen "the right to employment or . . . an income sufficient to meet basic human needs," and liberalized defendants' rights in criminal proceedings.

"The ultimate question is who will make the changes," said Fauntroy legislative aide Julius Hobson Jr. "Will they be made on the Hill or by the city?"

The D.C. City Council and the mayor could propose amendments or the city could leave it to Congress to make revisions, but in either case, the changes would have to go back to District voters for approval, city officials have said.

Aside from the substance of the constitution, at issue is the politics of the city, which would be expected to elect two Democratic senators and one Democratic representative if made a state.

"It's clear to everybody that, beyond the merits of statehood, as long as the Republicans control the Senate, you can forget it," Hobson said. At one point, a strategy was considered to pair statehood for the District with statehood for Puerto Rico--which would be expected to vote Republican--but that bogged down because Puerto Ricans have shown only half-hearted support for statehood, he said.

Charles I. Cassell, president of the statehood convention, yesterday put the best face on prospects for the statehood petition and constitution once they get to the Hill.

"We are more concerned with demonstrating that Washington, D.C., is united and determined to leave unrepresentative government behind us," he said when asked about the odds of passage in the next few years.

"We think Congress wouldn't stand for long against the will of an entire city," he added.

Cassell also said the convention delegates "stand ready to make changes as necessary," noting that the U.S. Constitution has been amended several times and predicting that "this one will be too."

The convention has "very, very little money," and that is one of the main reasons it took so long to get the constitution ready for submission to Congress, he said.

The news conference was held on the steps of the District Building yesterday and featured the Buck Hill Quartet as well as four statehood songs written by Cassell.

"It's time for Statehood / In Washington, / It's time for Statehood / Let's get on with it right now!" was one set of lyrics, sung to the tune of "Hail to the Redskins."