Hercules Dousman was the original Democratic nominee, but declined the party's nomination. The stated total for Dousman is 865 but the county figures add up to 824.
Candidates' party affiliations obtained from the 1862 Legislative Manual. https://search.library.wisc.edu/digital/AXU6B3ZTECZLNP8P/pages/ADUOAG4WPM5D7O8Z
Source for Popular Vote data: Wisconsin Board of State Canvassers, "State Treasurer," Tabular Statement of the votes...at the General Election (Madison, 1861)