Births and Deaths were recorded in Olmsted County starting in 1871?. i'd contact the Olmsted County Recorder to verify if they were or weren't recording deaths in 1870.
Hopefully the parents names will be in their obituaries. I'd contact the following:
History Center of Olmsted County, www.olmstedhistory.com/
Olmsted County Genealogical Society
PO Box 6411
Rochester 55903-6411 or 507-282-9447