The poll from the Quinnipiac University Polling Institute has the first lady favored by 46 percent of voters surveyed while the Republican congressman from Long Island was the pick of 43 percent of voters.
Given the poll's margin of error - plus or minus three points - the race remains a statistical dead heat. A July poll from Quinnipiac had Clinton and Lazio tied at 45 percent each.
Clinton and Lazio are both fighting for an increased share of the important Jewish vote. Jews make up about 12 percent of the voting population in New York. Recent events, including Al Gore's selection of Sen. Joe Lieberman, an orthodox Jew, as his running mate, have focused renewed attention on how Jews will vote in the Senate race.
According to the poll, four of five voters questioned said they had heard of allegations in a new book that the first lady used an anti-Semitic remark in 1974. Voters were evenly split on whether they believe her denial.
In an interview with CBSNews.com, Maurice Carroll, director of the Quinnipiac University Polling Institute, said the results suggested that alleged remark was not important to voters. Among those who believe she made the remark, 88 percent said it wouldn't affect how they vote.
Also, having Lieberman as Gore's running mate on the national ticket may help the first lady. Carroll recalled that, in 1989, when African-American David Dinkins was running for mayor, ethnic pride helped bring black voters to the polls. Dinkins was elected. If the Jewish community comes out to vote for Gore, many Jews are also likely to also vote for the first lady. In a close race, those votes could make the difference.
"For years, support of Israel has been a must in New York elections and Mrs. Clinton outscores Rep. Lazio slightly on this issue. Almost half the voters just don't know where he stands on Israel," said Carroll.
An issue Carroll thinks is sure to be an important factor is abortion. Despite his claims, "people are not convinced Lazio is pro-choice," said Carroll.
"Our numbers show that a candidate's position on abortion is very important. New York is pro-choice and New Yorkers doubt that he'd be a strong supporter of abortion rights," Carroll said.
Carroll said that the "one factor you can't put in a poll," - but that can't be overlooked - is the conventions.
"Lazio was not seen (during the GOP convention), while Hillary will be highly visible" at the Democratic convention, she said.
And the "big negative on Lazio is that he has not established his presence yet." Carroll said the question that should be asked next is, "Can the seat held by Sen. Daniel Patrick Moynihan be occupied by someone with as little visibility as Lazio?"