Sarah, duchess of York, arrived in the United States aboard the Concorde yesterday. Francis Cornish, the head of British Information Services in New York, warned 100 reporters covering the visit not to shout out questions about whether she is pregnant, a subject of great debate in British tabloids.

"She doesn't want to discuss private things. She seems to be asked endlessly about whether she is pregnant. We are asking people to bear in mind that this is her royal highness and to behave with a degree of restraint and courtesy."

The duchess arrived in New York and went immediately by helicopter to Waterford, Conn., for a charity appearance on behalf of the Eugene O'Neill Theater Center. In keeping with the theme of her visit, which includes attending a benefit performance of "The Phantom of the Opera" in New York, the duchess was given a puppet of the Phantom, which she quickly learned to use to taunt the media.

"Maybe I'll be a puppeteer one day," she joked.

Tahnee Welch Mugged

Raquel Welch's 26-year-old daughter Tahnee was mugged on a street on Manhattan's East Side yesterday, but one of the two robbery suspects was captured by bystanders minutes later.

Welch, who lives in New York and starred in the film "Cocoon," was knocked to the ground in front of an apartment building by the attackers, who ran off with her purse at 12:40 a.m. One suspect fled but the other was held by two unidentified witnesses until police arrived.

The captured suspect, a Brooklyn teen-ager, was charged with second-degree robbery.

Welch was taken to New York Hospital-Cornell Medical Center, where she was treated for lacerations to her right eye and scrapes on her hand, authorities said.

The Sominex Set

Actor-bodybuilder Arnold Schwarzenegger, Internal Revenue Service chief Lawrence Gibbs and President Reagan were ranked among the 10 dullest Americans of 1987 yesterday by International Dull Folks Unlimited.

J.D. (Dull) Stewart, an Eastman Kodak Co. pricing analyst in Rochester, N.Y., who serves as Dull Folks "chairman of the bored," called 1987 the Year of the Dullard when announcing his sixth annual awards.

"Dull acts abounded everywhere in the country, particularly in the Washington, D.C., area," said Stewart. In addition to Reagan and Schwarzenegger, recipients of the "Dull Brain Awards" for 1987 were fired White House aide Lt. Col. Oliver North and disgraced PTL founders Jim and Tammy Bakker. A special "Dull Lifestyle Award" was bestowed on CBS Evening News anchor Dan Rather.

'Cap's' Class Act

Former U.S. defense secretary Caspar Weinberger has been appointed a distinguished visiting professor at Edinburgh University this summer, it was announced yesterday.

Weinberger,who resigned from the Cabinet last fall, will spend four weeks at the university taking part in a special project called Tech 88, which will investigate the interplay among technology, communications and the humanities. He will join seminars and discussions and give a public lecture on the subject of freedom and technology.

The Dublin 'Cowboys'

Irish rock star Bob Geldof is jumping back into film work. The former leader of Ireland's Boomtown Rats rock group, who starred in Alan Parker's "The Wall" and Les Blair's "Number One" before turning his energies to spearheading the Band Aid/Live Aid African famine relief projects, is now set to direct "Cowboys," a story about contemporary life in Dublin. Geldof, who wrote the script, will not appear in the feature but will work with producer Steve Wooley, who directed "My Beautiful Laundrette."