Acting Attorney General Barbara Underwood is considered by some to be the favorite to serve out the remainder of disgraced former Attorney General Eric Schneiderman's term.
"I definitely think it should be an open process", Barclay said "There's a concern whenever the legislature gets to make an appointment to a statewide office - you don't want a backroom deal".
Underwood credited her experience as distinguishing her from the other applicants, "I believe that, at this critical time, the attorney general must be a stabilizing and strong voice for the rule of law", she said.
Schneiderman resigned last week following a report by The New Yorker magazine that he physically abused four women he had dated. Schneiderman denies the allegations.
Rice and fellow New York Rep.
A spokeswoman for the attorney general's office tells News 12 that they are well within their legal right to pursue the charges.
She was one of seven candidates scheduled to interview Tuesday, including Assemblyman Thomas Abinanti of Westchester County, with another six candidates scheduled for Wednesday.
Another applicant, Elizabeth Holtzman, is a former congresswoman who served on the House Judiciary Committee that oversaw the impeachment of President Richard Nixon and co-founded the Congressional Caucus for Women's Issues in 1977.
Another concern for Rice was she could face scrutiny for potential campaign finance violations if she ran for attorney general.
Candidates interested in the attorney general's job but who skipped the interview process include New York City Public Advocate Letitia James; Zephyr Teachout, whom Cuomo defeated in the 2014 Democratic gubernatorial primary and state Sen. Michael Gianaris, of Queens.
"G$3 iven the timing of Eric Schneiderman's resignation and the current state law prohibiting candidates from seeking two offices simultaneously, I have determined that I can not run for Attorney General at this time", she said.
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