Date and place of birth would be nice - even if it were an estimate
Date and place of death would be nice - even if it is an estimate
Winona, KS is in Logan County.
Her mother is buried here. Others are not in find-a-grave here, but they may still be buried here:
http://www.findagrave.com/cgi-bin/fg.cgi?page=gr&GSln=Vo...;
Based on her mother's vital dates, there is a good chance that Verna may have a death certificate.
The second place to look for more about her and what caused her death might be an obituary. But, again, need a date to start looking. Unless Logan county has indexed obits somewhere. For obits, you can try the Kansas State Library in Topeka, which has (most) newspapers published in Kansas, a local source (call Logan library), or an on-line newspaper archive.
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Later:
Verna is 1 yr old in 1940 census with parents in Winona, Logan, KS
Do you think she married?