If you need to dig through news accounts of long-ago events (or if you just enjoy browsing), you're lucky that the University Libraries subscribes to lots of resources, including a digital version of the Seattle Times, 1900-1985, where I found this story. See the Libraries' News Guide.
The story about the King County workers mentions that the petition also protested the firing of Lea Puymbroeck Miller, a UW faculty member who was also a "working wife." Over 200 faculty members, meeting in the law school building, passed a resolution asking that the UW reverse itself, but the Board of Regents unanimously refused. For more, see Claire Palay, Lea Miller's Protest: Married Women's Jobs at the University of Washington and Married Women's Right to Work: "Anti-Nepotism" Policies at the University of Washington in the Depression (2009).