The survey of registered New York voters by the Quinnipiac University Polling Institute showed Lazio and Clinton each with 44 percent.
The last time Quinnipiac checked the New York Senate race was in a poll released on May 16, when it found Clinton with 44 percent and New York City Mayor Rudolph Giuliani with 43 percent. Three days later, Giuliani dropped out of the race to fight prostate cancer and Lazio, a Long Island congressman, declared his candidacy the same day.
Maurice Carroll, director of the Quinnipiac institute, said the poll is "surprising good news" for Lazio.
"New to the Senate race, he's in a dead heat with Mrs. Clinton and already on par with the Republican he replaced," Carroll said.
The poll was conduced by telephone from May 30-June 5 and has a margin of error of plus or minus 3 percentage points.