Republican George Bush, facing a deadline in three weeks to announce his running mate, is stepping up his search, asking candidates if they're interested in being considered and planning to use polling to determine the popularity of different people.

The list of possible candidates was expanded Tuesday when Gov. John Sununu of New Hampshire said he had received questionnaire forms that Bush is using in his search. Bush already had said that Senate Minority Leader Bob Dole of Kansas would be among those considered.A Bush campaign official said the staff was contacting various people to see if they wanted to be considered.

"Preliminary interest is being ascertained. I think you're safe to assume it's more than John Sununu," the official said.

Within Republican circles, others considered as likely candidates include Rep. Jack Kemp of New York and California Gov. George Deukmejian, even though he has said he is not interested.

Washington lawyer Robert M. Kimmitt has been asked to begin background checks on several potential vice presidential picks, The Washington Post reported in Wednesday's editions.

Bush told the newspaper that Kimmitt will report directly to him rather than the campaign staff, to better maintain confidentiality of the information provided by the prospective running mates.

Kimmitt is a native of Ogden, Utah; a graduate of West Point and Georgetown Law School, and a veteran of 17 months in Vietnam. In addition to enjoying a close relationship with Bush and Secretary of the Treasury James A. Baker III, who is expected to leave the Cabinet next month to head the Bush campaign, Kimmitt has been an important volunteer worker on Republican platform and policy issues.

Rep. Lynn Martin, R-Ill., co-chairwoman of Bush's campaign committee, said it's clear that some women are being considered.

"One of the nicest surprises for me is hearing . . . many conservative members of my party talking about a woman on the ticket as a good idea," said the congresswoman, whose name has appeared on some public lists of possible running mates.

She said other strong candidates include former Transportation Secretary Elizabeth Dole, Sen. Nancy Kassebaum of Kansas, former U.N. Ambassador Jeane Kirkpatrick and Nebraska Gov. Kay Orr.

However, Rep. Martin said the selection of a woman was "possible, not probable."

Bush, certain to be the Republican presidential nominee, has said he wants to keep his running mate a secret until the Republican National Convention, which opens Aug. 15 in New Orleans.

Despite the public speculation about his running mate, Bush trained his public focus on another subject Tuesday, delivering a speech at the Library of Congress before congressional interns about the ethical standards he would set if elected president.

He said Congress should be covered by the same conflict-of-interest laws that govern federal officials and that civil penalities as well as criminal sanctions should be used to punish violators.

Breaking with the Reagan administration, Bush also endorsed the use of independent counsels to investigate wrongdoing by federal officials and said Congress should come under the same law.

"To exempt Congress from any of these rules, as does current conflict-of-interest law, is to establish a double standard that breeds suspicion, breeds cynicism and, in my judgment, breeds abuse," he said. "No one, no institution, no body of government should be above the law."