Ms. Arnott's opponent in November will be San Mateo County Community College District board member Dave Mandelkern, who came in second in a four-way race.
The treasurer acts as a banker for county public agencies such as school and sewer districts. The treasurer also manages these agencies' investment portfolio, currently valued at about $2.6 billion. Lee Buffington, who has been the treasurer for 25 years, retires at the end of the year.
In the race, Ms. Arnott got 38 percent of the nearly 61,000 votes cast in county's 456 precincts, according to semi-official results from the registrar's office.
Mr. Mandelkern took second place with 17,000 votes, or 28 percent, the report said.
Bringing up the rear were certified public accountant Joe Galligan with 25 percent and investment adviser Richard Guilbault with 9 percent.
San Mateo County Coroner Robert Foucrault easily withstood a primary election challenge by Stacie Nevares, an analyst for the police department of the University of San California at San Francisco.
According to the latest count in the June 8 election, Mr. Foucrault received 50,767 votes, or 69 percent of the total. Ms. Nevares received 22,969 votes, or 31 percent of the total.