This was California's first popular election for State Treasurer. Richard Roman had been appointed as the state's first Treasurer in 1849.
The statement of vote does not list any votes for San Diego, San Francisco, Santa Barbara, and Solano counties. Votes from these counties were published in newspapers of the time and these counties are also listed on the separate abstract for Governor and Lieutenant Governor.
Candidates' party affiliations obtained from 9/24/1851 Sacramento Daily Union. https://www.cdnc.ucr.edu/?a=d&d=SDU18510924.2.9.1&e=-------en--20--1--txt-txIN--------
Source for Popular Vote data: California State Archives, "State Treasurer," Statement of the Returns of the General Election held for the State of California on the third day of September A.D. 1851 (Vallejo, 1851)