Former police chief Maurice T. Turner Jr. and Del. Walter E. Fauntroy (D-D.C.), testing the fund-raising waters for the first time this year, got off to a good start in their efforts to finance their mayoral campaigns.

Turner, a Republican, collected about $205,000 and Fauntroy raised $184,000 in the first three months of their campaigns -- more than any of their rivals for the comparable period, according to campaign finance reports filed last week with the D.C. Office of Campaign Finance.

Although both candidates still lag behind the fund-raising leader, D.C. Council member John Ray (D-At Large), who has collected nearly $700,000 since last year, their performances suggest that they should have sufficient funds to wage competitive campaigns.

Both are being aided by party fund-raisers with national reputations. Wally Ganzi, a prolific GOP fund-raiser in 1988, is helping Turner and lawyer Terry McAuliffe, who was a fund-raiser for Rep. Richard Gephardt's presidential campaign and former House Democratic whip Tony Coelho, is working for Fauntroy.

Turner, who has said he wants to raise $2 million for his campaign, appears to be relying heavily on the national Republican fund-raising network for funds, with businesses and executives from around the country donating funds. The GOP, hoping to make inroads among blacks, has made the District a priority in the 1990 elections. Turner has visited President Bush in the White House on at least two occasions.

Ganzi forked over $2,000 to Turner, as did another Republican fund-raiser, Wyatt Stewart, whose consulting firm also contributed $2,000. The National Republican Congressional Trust and National Republican Senatorial Committee each contributed $2,000.

Other contributors giving the maximum $2,000 include W. Clement Stone Enterprises of Lake Forest, Ill., a firm started by the insurance magnate and former donor to Richard M. Nixon; Sun Diamond Growers of California; Kenneth Clarke, president of Sentury Federal Savings Bank of Virginia Beach; Winthrop Paul Rockefeller of Little Rock, Ark.; and James E. Burke, of New Brunswick, N.J., chief executive officer of Johnson & Johnson, and his wife, Diane.

Locally, Turner collected $2,000 from stockbroker Thomas D. Walsh and Andy Ockershausen, manager of Channel 50, and $1,000 from the D.C. National Bank Political Action Committee.

Turner also collected about $40,000 from a testimonial dinner held last year, including $250 from American Security bank chief Daniel Callahan, $500 from Parking Management Inc., $250 from Dale Denton Real Estate and $250 from developer Kingdon Gould.

Fauntroy, meanwhile, showed success raising funds from some of his colleagues in Congress and other national figures, as well as from a group of longtime supporters and local business executives.

The campaign committees for Democratic Reps. Joseph P. Kennedy II (Mass.), Charles Rose (N.C.), Mike Espy (Miss.), Louis Stokes (Ohio) and Charles B. Rangel (N.Y.) each gave Fauntroy $1,000, as did former Democratic Maryland representative Michael Barnes.

Fauntroy collected $2,000 donations each from lawyer and friend Wright Andrews, lawyer James Christian, lawyer Ruby B. McZier and from Robert L. Johnson, head of Black Entertainment Television. Three of Johnson's companies also kicked in $2,000, as did hardware magnate John W. Hechinger and his wife, June.

Also, Chesapeake & Potomac Telephone Co. President Delano E. Lewis, a longtime supporter of Mayor Marion Barry, contributed $1,000 to the Fauntroy effort.

While Fauntroy has criticized John Ray for taking contributions from developers, he showed no reluctance in accepting real estate money, showing a $250 contribution from zoning lawyer Whayne Quin, $500 from Quin's firm, $500 from the Donohoe Cos. and $2,000 each from Fort Myer Construction Co. and Prince Construction Co. Elsewhere on the Campaign Trail

Mildred Goodman, a Ward 4 member of the D.C. Democratic State Committee who directed the Dukakis presidential campaign in the District in 1988, has defected from the mayoral campaign of Charlene Drew Jarvis to join the campaign of Sharon Pratt Dixon. Goodman says she is switching sides not because she is disenchanted with Jarvis, a Ward 4 D.C. Council member, but because she is impressed with Dixon's campaign.

"She's coming up with fresh approaches," Goodman said. "People don't seem to be listening, and I want to try to turn that around."

In another race, Eleanor Holmes Norton has picked up the endorsement of influential churchman Bishop Smallwood Williams, pastor of Bible Way Church, in her campaign for D.C. delegate to Congress. Williams, a longtime supporter of Barry and Fauntroy, has also been named co-chairman of Norton's campaign.

Norton was also recently endorsed by Americans for Democratic Action.

Meanwhile, the Metropolitan Washington Council of the AFL-CIO has delayed its decision for a monthon who to endorse in races for mayor and delegate. The council's board, apparently divided over who to back, has decided to poll its members to see who commands support for the important labor endorsements.