In 1995, Murray, a Democrat, ran to fill the state Senate seat left vacant by the death of Anderson, his mentor. Murray was defeated by state Representative Pat Thibaudeau, but was then appointed to fill Thibaudeau's vacant state House seat in the 43rd Legislative District. He was reelected biennially until 2006, when he opted not to run for reelection to the House. The 43rd district, entirely within Seattle, includes the University District, Montlake, Eastlake, and Capitol Hill neighborhoods. The district is very progressive and reliably Democratic.