WASHINGTON (AP) _ The first finance reports of the presidential race show Lamar Alexander raising most of his money in his native Tennessee, Bob Dole doing well among former top government officials and Phil Gramm outpacing them both with $8 million in contributions.

Alexander's initial report, covering the period from Jan. 1 through March 31, is top-heavy with Tennessee money, the product of a series of fund-raisers there. About $3.2 million of his $5.2 million so far is from his home state.

Senate Majority Leader Dole, the early front-runner in the GOP race, shows receipts of $4.4 million. His report includes donations from lobbyists, former Cabinet secretaries and current and former members of Congress. He's also drawn contributions from the ranks of the federal bureaucracy.

Gramm has gotten money from everywhere, raising $8 million and leaving no state untouched _ but, like Alexander, drawing heavily from his home state.

Meanwhile, it is evident that seasoned politicos _ inside the Beltway and out _ are playing it cautious at this early stage of the campaign. That means being generous to more than one candidate.

For example, Alexander has received $1,000 contributions from former Nixon aide and Bush campaign official Fred Malek and his wife. But Dole, too, has received $2,000 from the couple.

Likewise, former Bush Commerce Secretary Robert Mosbacher and his wife, Georgette, have donated $1,000 apiece to Alexander, who also served in Bush's Cabinet. But they've given $1,000 apiece to Dole, too.

The same is true of former State Department official Abraham Sofaer, who gave $1,000 each to Dole, Alexander and Gramm.

Gramm campaign officials noted that the Texas senator had received donations from all 50 states.

``This isn't just regional, this isn't just small donors and this isn't just large givers,'' Gramm spokesman Gary Koops said. ``We've got almost 50,000 donors, and they come from all over the country.''

While Gramm has yet to pick up many contributions from Reagan and Bush administration officials, he has received $1,000 apiece from actor Kevin Costner, chicken magnate Frank Perdue, Arizona Gov. Fife Symington and Watergate figure Donald Segretti.

Gramm also got $1,000 each from Jerry Reinsdorf, owner of the Chicago White Sox; Wayne Huizenga, who owns the Florida Marlins, and former Dallas Cowboys quarterback Roger Staubach. Alan Roth, president of the National Review, has given $500 to Gramm.

Alexander spokesman Dan McLagan said that despite the heavy concentration of in-state money, the former Tennessee governor and Bush administration education secretary has done well raising cash in other places in recent weeks _ a fact not reflected on those reports.

``We're doing very well all over the place, but Tennesseans know Lamar, and they know what a great governor he was, and they're leading the charge,'' McLagan said. ``That's good _ the people who know him best are giving lots of money, not sitting on the sideline.''

McLagan said that the vast majority of the Tennessee contributions came from three fund-raisers _ in Nashville, Knoxville and Memphis _ that he said raised a combined total of about $3.2 million.

Among Alexander's early backers: Robert S. ``Bud'' McFarlane, a figure in the Iran-Contra scandal, pop music star Amy Grant, Corporation for Public Broadcasting president Richard Carlson, and former acting Attorney General Stu Gerson.

Dole, meanwhile, has attracted $1,000 donations from Prescott Bush, brother of the former president, C. Boyden Gray, Bush's White House counsel, Nixon White House counsel Fred Fielding, Reagan Transportation Secretary Drew Lewis, and Brent Scowcroft, Bush's national security adviser.

He has also received $1,000 donations from former Sens. Roger Jepsen of Iowa and Paul Trible of Virginia, as well as $1,000 contributions from beer barons August Busch III and Peter Coors. Former Defense Secretary Frank Carlucci has contributed $500.

Dole has also received $1,000 from Sheila Bair, a commissioner on the Commodity Futures Trading Commission. Bair, a Kansan, worked as an attorney for Dole in his Senate office in 1986 and 1987. Wendy Lee Gramm, wife of Phil, headed the CFTC until January 1993.