He was a Labor Party member of the New South Wales Legislative Assembly from 1982 to 2003, representing the electorate of Drummoyne.
Murray was involved in local branch politics, and won Labor preselection to contest the local seat of Drummoyne at a 1982 by-election caused by the resignation of sitting MLA Michael Maher to enter federal politics.
He was easily elected, as Drummoyne was considered a safe Labor seat, and re-elected five more times.
[1] Even though Murray became Speaker as a result of his party holding majority government, Liberal Opposition Leader Peter Collins made issue of Murray's election as Speaker, saying that Murray's election was illegal since some ALP members showed their ballot papers to each other, which contravened recent changes to the Constitution.
Leader of the House, Paul Whelan, said Collins had not raised an objection at the time of the ballot.