After having failed in her first attempt to run for office against incumbent City Councilman Samuel Horowitz in the 33rd district of New York City in 1989, Cohen made her second run for office in the 1991 Democratic primary election for New York City Council District 48 in Southern Brooklyn, which had been created as part of the expansion of the city council membership prior to the election. She ran in a tightly contested six-way Democratic primary that included both Anthony Weiner, the future Congressman who was then a congressional aide to U.S. Senator Chuck Schumer, and Michael Garson, who was endorsed by the Kings County Democratic County Committee, representing a labor-dominated coalition known as the Majority Coalition for a New New York. Controversy erupted in the last weeks of the campaign, however, when Weiner's campaign anonymously spread leaflets around the district which alleged ties between Cohen and the so-called "Jackson-Dinkins agenda." The leaflets referred to the Crown Heights riots earlier in the year, which suggested that Jesse Jackson and mayor David Dinkins as having been beholden to the predominantly-African-American rioters, and thus endangering white residents. Dinkins, during the campaign, described the leaflet as "hateful". When Weiner admitted his campaign's distribution of the leaflets, he stated that he "didn't want the source to be confused with the message"; The New York Times issued an editorial which rebuked Weiner's "hit-and-run tactics". Cohen lost the primary to Weiner by 195 votes. Weiner also won the November election, widely considered a formality with no opposition in the heavily Democratic district. The next year, Cohen was selected as the state chairwoman of the National Women's Political Caucus. She ran again for the City Council's 27th District against Howard L. Lasher in 1997, but lost in the three-way Democratic primary.
State Assembly
In 1998, Cohen ran for the New York State Assembly's 46th district in the special election to succeed outgoing assemblyman Jules Polonetsky, with the nomination of the Democratic, Independence and Liberal parties and she won against Joseph A. Kovac, a nominee of the Republican and Conservative parties. She served as an assemblywoman until she returned to private law practice in 2006. Initially a member of the Standing Committee on Insurance, she served from 2005 to 2006 as chairwoman of the Assembly Commission on Science and Technology during her time in office.
