The study described here investigates the extent to which something resembling auditing may have existed or may even have been required by state law. (Most banks which existed had some sort of state or territorial charter before 1863, prior to the creation of a federal central banking system.)
"Some observations on the extent of bank audits in America: 1800-1863,"
Accounting Historians Notebook: Vol. 12
, Article 19.
Available at: https://egrove.olemiss.edu/aah_notebook/vol12/iss1/19