Katherine Mull was born in Muscatine, Iowa on March 19, 1904. She graduated from Muscatine High School in 1922 and from the University of Iowa in 1926. In 1925 she married Lawrence A. Falvey and moved with him to Albia, Iowa where he managed the family farm and lumber business as well as the First Iowa State Bank. Lawrence Falvey served from 1953 to 1957 as a representative from Monroe County to the Iowa General Assembly. Upon her husband's death, Katherine Falvey assumed the oversight of the Falvey family farm, lumber business, and the First Iowa State Bank.

At the urging of friends, Falvey ran successfully as a Democratic candidate to fill her late husband's seat in the legislature. She held this seat from 1958 to 1964. Falvey served on the education committee, the library subcommittee, and the mining committee, among other assignments during her tenure in the legislature. In 1961-1962 she served one term on the Iowa Development Commission. She married Ralph A. Zastrow, a Charles City lawyer and former Iowa state senator, in 1963.

Following Ralph Zastrow's death in 1965, Katherine Zastrow was appointed to the Iowa Library Commission for northeast Iowa and served one term. In 1970 she became the first woman elected to the Charles City Council. She was a member of the State Advisory Council on the Title 1 program of the United States Department of Health, Education, and Welfare. Active in public library support throughout her life, Zastrow served many years on the Charles City Library Board.