Need more information to narrow things down a bit. Seems Catherine McKenzie is a pretty common name. There are even people of different races with the same name during that time period. Do you have a geographical area? That would help. In the meantime, here is a sample of only a few things I have found:
Califonia Death Index 1940-1997 has Catherine McKenzie Dangelo b. 10 Feb 1909 in "Other Country" and died 17 Fe 1981 in Los Angelos. Mother's maidenname was McAvoy
Social Security Death Index 1935-current lists Catherine McKenzie b. 4 Aug 1910; d. Jan 1980 Bronx, New York.
1930 US Federal Census lists Catherine McKenzie b. abt 1910 in Scotland; worked as a maid in the home of Walker Smith and family. Immigrated to US in 1929 at age 19. Parents born in Scotland. She was single at this time.
1940 US Federal Census lists Catherine McKenzie. b. abt 1910 in Georgia, US. Negro. Working as a cook in Augusta, Richmond, Georgi. Lived or worked at 1028 Agnes St. Lived at "Colored Old Falcon Town"
West Virginia, Marriages Index, 1785-1971 lists Catherine McKenzie b. abt 1909 and married to John Lester Kirk Oct 10, 1934. Father was Clarence McKenzie;mother Catherine.
So many directions to look at. Can you possibly narrow it down or have more to go on. Her profile is pretty scant....Good luck in your quest.. Patti