Answer by taking a quote from the following article:

Giuliani was born in an Italian-American enclave in East Flatbush in the New York City borough of Brooklyn, the only child of working-class parents, Harold Angelo Giuliani (1908-1981) and Helen Giuliani (nee D'Avanzo; 1909-2002), both children of Italian immigrants. Giuliani is of Tuscan origins from his father side, as his paternal grandparents (Rodolfo and Evangelina Giuliani) were born in Montecatini, Tuscany, Italy. He was raised a Roman Catholic. Harold Giuliani, a plumber and a bartender, had trouble holding a job, and was convicted of felony assault and robbery, serving time in Sing Sing.

Due to term limits, Giuliani could not run in 2001 for a third term as Mayor. In November 1998, four-term incumbent Democratic U.S. Senator Daniel Patrick Moynihan announced his retirement and Giuliani immediately indicated an interest in running in the 2000 election for the now-open seat. Due to his high profile and visibility Giuliani was supported by the state Republican Party. Giuliani's entrance led Democratic Congressman Charles Rangel and others to recruit then-U.S. First Lady Hillary Clinton to run for Moynihan's seat, hoping she might combat his star power.  An early January 1999 poll showed Giuliani trailing Clinton by 10 points. In April 1999, Giuliani formed an exploratory committee in connection with the Senate run. By January 2000, Giuliani had reversed the polls situation, pulling nine points ahead after taking advantage of several campaign stumbles by Clinton. Nevertheless, the Giuliani campaign was showing some structural weaknesses; so closely identified with New York City, he had somewhat limited appeal to normally Republican voters in Upstate New York. The New York Police Department's fatal shooting of Patrick Dorismond in March 2000 inflamed Giuliani's already strained relations with the city's minority communities, and Clinton seized on it as a major campaign issue. By April 2000, reports showed Clinton gaining upstate and generally outworking Giuliani, who stated that his duties as mayor prevented him from campaigning more. Clinton was now 8 to 10 points ahead of Giuliani in the polls.  Then followed four tumultuous weeks, in which Giuliani's medical life, romantic life, marital life, and political life all collided at once in a most visible fashion. Giuliani discovered that he had prostate cancer and needed treatment; his extramarital relationship with Judith Nathan became public and the subject of a media frenzy; he announced a separation from his wife Donna Hanover; and, after much indecision, on May 19, 2000 he announced his withdrawal from the Senate race.

Did he win?
after much indecision, on May 19, 2000 he announced his withdrawal from the Senate race.