Answer by taking a quote from the following article:

Dixy Lee Ray (September 3, 1914 - January 2, 1994) was an American scientist and politician who served as the 17th Governor of the U.S. state of Washington. Variously described as idiosyncratic, and "ridiculously smart," she was the state's first female governor and was governor during the 1980 eruption of Mount St. Helens. She was a supporter of atomic energy. A graduate of Mills College and Stanford University, where she earned a doctorate in biology, Ray became an associate professor at the University of Washington in 1957.

To the surprise of many, Ray announced in 1975 she would seek election as Governor of Washington. Later asked why she decided to make her first run for public office the highest office in the state, she would reason that "I was much too old to start at the bottom, so I decided to start at the top." Though previously politically unaffiliated, she declared herself a Democrat.  Ray displayed a blunt, sometimes confrontational, style on the campaign trail, for which she would later become known. During a visit with the Dorian Society, a Seattle gay rights group, she was asked by one member if she had met any gay federal employees and if they ever felt under pressure. Ray responded, "I don't know any - you can't tell by looking at them," drawing applause from attendees. In another instance, she declared Seattle Post-Intelligencer reporter Shelby Scates, who had deluged her with tough questions on the campaign trail, would "learn what the words persona non grata really mean" after her election.  Ray narrowly won the Democratic nomination over Seattle mayor Wes Uhlman, having spent almost no money on her campaign, having no experience in running for elected office, and having little support from the state's political class. Despite opposition from all major newspapers and predictions from pundits that the state was not ready "for an unmarried woman who gave herself a chainsaw for Christmas," Ray went on to win the general election with a victory over King County Executive John D. Spellman, 53%-44%. On election night, asked by a reporter to explain her surprise victory, she offered, "it can't be because I'm so pretty?"

Was she running as republican or democrat?
Though previously politically unaffiliated, she declared herself a Democrat.