Birth surname might be Schmidt rather than Smith, but no direct evidence has been found yet.
A note in Anna Maria's great-grandson George Peterson's biography says that Anna Maria's mother was kidnapped and held for seven years by Indians during the Revolutionary War and died soon after her release; no confirmation of this story has been found yet, however.
Sources
Research of Lee Garlock
Biography of great-grandson George Henry Peterman, in Album of Genealogy and Biography, Cook County, Illinois (Volume 1897), pp 55-56.
Thank you to Sharon Casteel for creating WikiTree profile Smith-53183 through the import of slc2.ged on Oct 22, 2013. Click to the Changes page for the details of edits by Sharon and others.
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DNA Connections
It may be possible to confirm family relationships with Anna Maria by comparing test results with other carriers of her mitochondrial DNA.
However, there are no known mtDNA test-takers in her direct maternal line.
It is likely that these autosomal DNA test-takers will share some percentage of DNA with Anna Maria: