D.C. Council member Carol Schwartz (R-At Large), charging that "we are overtaxed and underserviced," announced her candidacy for mayor yesterday, becoming the first ranking official to challenge Mayor Marion Barry.

"I think I am a credible candidate," the 42-year-old lone Republican on the council said. "I think the mayor will consider me a credible candidate."

Schwartz conceded she may be an underdog -- a white Republican in a city where registered Democrats outnumber Republicans 10 to 1 and blacks make up 70 percent of the population. But she said the issues of taxation and city services cut across race and party lines.

"I stand a chance because there is no Republican or Democratic way to pick up trash," said the first-term council member, who previously served on the D.C. school board. "There is no white way or black to fix our potholes or to create work for our youth."

Schwartz, accompanied by her husband David and her three children, sharply criticized the Barry administration for rampant "waste, incompetence and inefficiency" in housing, corrections, youth services and other programs.

"I am running because I cannot accept an administration which spends millions of dollars on 'consultant contracts' for cronies, but cannot find the money to answer the police emergency phone lines," she said.

Schwartz avoided using the term "corruption," explaining that she does not want to run an "inflammatory" campaign. An aide said the council member believes voters are more concerned about waste than the last year's spate of reports of wrongdoing by Barry administration officials.

Schwartz also emphasized the issue of taxation, calling the District the most overtaxed jurisdiction in the United States, and blasting Barry for property assessments that have boosted taxes even as the tax rate has remained stable.

Schwartz is the first announced candidate for the Sept. 9 Republican primary. She is not up for reelection to her at-large council seat until 1988 and will not have to relinquish it to run for mayor.

Schwartz's decision to run for mayor, which she said she made late Monday night, caught many political observers by surprise.

Previous speculation on major candidates opposing Barry had centered on D.C. Council Chairman David A. Clarke and council member John A. Wilson (D-Ward 2), but both have opted not to enter the race.

An aide to Clarke said yesterday Schwartz's decision "has no effect" on Clarke's plans.

Barry aides earlier had said that Schwartz was testing the waters for a possible run, but in an interview last week she denied it, saying that she had been encouraged by supporters in recent months to run but didn't anticipate doing so.

"I have been talking to friends, to close friends," she said yesterday."The odds are probably against me but I believe people do deserve a choice. I will provide a viable, credible campaign."

Schwartz begins the race without an organization, funds or a strategy in the face of what she expects will be opposition from her colleagues on the council, she said yesterday.

However, some observers believe Schwartz remains in an enviable position.

"She certainly doesn't have anything to lose and everything to gain," observed council member John Ray (D-At Large). "This will give her a platform to get her views before the public . . . . Even if she didn't secure the mayor's seat, she could come out a winner."

Four years ago, Barry easily defeated challenger Patricia Roberts Harris in the Democratic primary and Republican E. Brooke Lee in the general election.

This year, until yesterday's announcement, he faced a gallery of relatively unknown challengers. Barry will have a hard time ignoring Schwartz, Ray said.

"She is at-large. She is going to raise some money. She is going to have some visible support that the other mayoral candidates don't have. I don't think the mayor can totally ignore her," Ray said.

Other Democrats reacted to Schwartz's announcement more negatively.

"Before aspiring to the highest elected job in the District, she would be well advised to spend more time learning her job and how the council operates," said retiring council member Polly Shackleton (D-Ward 3).

James Christian, chairman of the D.C. Democratic State Committee, dismissed Schwartz's mayoral aspirations as a pipe dream.

"Carol is a very capable person, but a Republican running for mayor in this town would be more of a symbolic race than one with any efficacy," he said.

Ann Heuer, chairman of the D.C. Republican Committee, said the local GOP "will support her 100 percent. I am very pleased."