The flag of the famous state of Arkansas, birthplace of the 42nd president of the United States, flew in all its red brilliance today over New York City Hall. It was, said Republican Mayor Rudolph W. Giuliani, a simple "act of reciprocity." Arkansas flew a New York flag when Giuliani visited there Tuesday, so Giuliani just wanted to do the same in return.

Yeah, right, New York Democrats say. Tell it to my dog.

Flapping like a banner of war, the Arkansas flag drew howls of protest from state and local Democrats. It was, they said, a misuse of mayoral power as well as a political swipe at first lady Hillary Rodham Clinton -- she of Illinois and Arkansas -- for being a non-New Yorker seeking to represent New York in the U.S. Senate. A seat, by the way, that Giuliani also has his sights set on.

A universe separates New York from Arkansas, and in highlighting that difference Giuliani seemed to be underscoring the issue that Clinton's supporters must contend with most: that she is perceived as a carpetbagger come to New York, a foreigner with a big name but with no personal roots in the state.

Neither Giuliani nor Clinton is a declared candidate. The election is about 16 months away. But already, this race to replace the retiring Sen. Daniel Patrick Moynihan (D) threatens to be New York political theater of the highest order. Polls show Giuliani leading Clinton by 5 to 10 percentage points.

Clinton established an exploratory committee earlier this month to raise money for a Senate bid. Then she launched a series of "listening tours," mostly of upstate and suburban towns, to get to know New Yorkers' concerns and show her empathy.

So unprecedented and high profile has this nonofficial campaign become that every step, misstep, even nonstep along the way has received thorough news coverage. The New York Observer, a highbrow weekly, noted that Clinton, during one of her "listening events," seemed to feel the pain of her guests so keenly that she nodded like an automaton, 43 nods in one minute, and "inadvertently hypnotized an audience with her head."

Today, Clinton's operation took it on the chin as stoically as it has since she began her New York effort. Rather than get involved in the flag flap, said Howard Wolfson, her exploratory press secretary, "Hillary Clinton is going to continue to talk to New Yorkers and focus on the issues."

The whole flag-flying flap stems from a joke Giuliani made several weeks ago about Clinton's potential Senate run. Maybe, he said then, he ought to seek public office in Arkansas, a state where he has as few roots as Clinton in New York, meaning virtually none. That was a tongue-in-cheek threat. But from it grew the idea of traveling to Arkansas to raise money. Then, while he was in Little Rock on Tuesday mocking Clinton's exploratory campaign, his people back in New York City ran the Razorback state flag up the pole at City Hall.

"I've never lived here, I've never worked here, I've never gone to school here, it's the first time I've been here. I guess it would be cool to run for the Senate," Giuliani reportedly said in Little Rock.

New York Democrats slammed his "joke" trip to Arkansas and said it raised questions about whether, in the Senate, he would support New York's interests or the interests of a broader "right-wing" agenda. Giuliani, who supports abortion rights and gay rights, is a more moderate Republican than Arkansas Gov. Mike Huckabee. But Huckabee said they have more in common than in opposition.

At the White House, spokesman Joe Lockhart said President Clinton was "probably as bemused as most everybody else here" about Giuliani's visit to Little Rock.

Back home in New York, where his abrasive style has earned him a plethora of political enemies, the flag flap raised hackles. Peter Vallone, the Democratic speaker of the New York City Council, wrote to Giuliani this morning with the "clear consensus" of council members. "We hereby respectfully order you to remove the state flag of Arkansas from the flagpole on City Hall," Vallone wrote to Giuliani.

The mayor's office responded in a letter that the city code "does not empower the City Council to direct the mayor to forbear from flying the flag without the passage of a local law." Samantha Lugo, a Giuliani spokeswoman, said the flag would come down at the close of business today, after being up for nearly two days -- the same amount of time New York's flag flew in Arkansas. Though state Republicans are likely to see a bruising Senate primary battle between Giuliani and Rep. Rick Lazio, at least for now the statewide party was amused at the flag-flapping antics. Dan Allen, party spokesman, wondered how Democrats could be so annoyed that a flag from Arkansas was flying here when Arkansas' most famous former first lady is their preferred candidate for Senate.

"They seem," he said, "to be talking out of both sides of their mouth."