Following law school, Murray clerked for
Sonia Sotomayor (then on the
Second Circuit) and
Stefan R. Underhill of the
United States District Court for the District of Connecticut. Murray joined the faculty at
UC Berkeley School of Law in 2006 and was granted
tenure in 2011. The following year, her article "What's So New About the New Illegitimacy?" was awarded the Dukeminier Awards' Michael Cunningham Prize as one of the best sexual orientation and gender identity law review articles of 2012. As a
full professor at UC Berkeley, Murray was the recipient of the 2014 Rutter Award for Teaching Distinction which "honors a professor who has shown an outstanding commitment to teaching and who is an inspiration to students." The following year, she was appointed faculty director of the
Center on Reproductive Rights and Justice (CRRJ), the United States' first law school think tank to focus on
reproductive rights and justice issues. She also became the co-author of "Cases on Reproductive Rights and Justice," the first reproductive rights and justice casebook. On March 22, 2016, Murray was named interim dean of the UC Berkeley School of Law following the resignation of former dean
Sujit Choudhry. On June 11, 2018, Murray left UC Berkeley to accept a position as a tenured faculty member at
New York University and become the co-faculty director of the Birnbaum Women's Leadership Network. On September 7, 2018, Murray testified at
Brett Kavanaugh's Supreme Court confirmation hearing where she cautioned the
United States Senate Committee on the Judiciary that he would overturn
Roe v. Wade. Murray has been a member of the
American Law Institute and sat on the boards of directors for the
Brennan Center for Justice, the
American Constitution Society, the
Guttmacher Institute, and the National Women's Law Center. Murray was considered to be a contender for a federal
judgeship under the
Biden administration. Since 2019, Murray has co-hosted the
podcast Strict Scrutiny with fellow legal academics
Kate Shaw and
Leah Litman. In 2022, the podcast joined the
Crooked Media network. ==Personal life==