The supervisors made the decision in a 4-0 vote on Tuesday, Dec. 14, said board spokesman Marshall Wilson.
Although District 1 is in the northern part of the county, and includes South San Francisco, San Bruno and Hillsborough, ballots will be mailed to all registered voters in the county because supervisors run county-wide.
Mr. Church is resigning his seat a little less than two years into his third term because voters elected him to replace Warren Slocum, the outgoing county clerk, recorder, and registrar of voters.
In November, 66 percent of county voters approved a measure that requires an election to replace the supervisor if the resigning supervisor leaves on or before Oct. 15 of the third year of the supervisor's four-year term.
Mr. Church's remains a supervisor until his Jan. 3 swearing-in for his new position, which is why he participated in the Dec. 14 vote by the Board of Supervisors, Mr. Wilson said.
The normally five-member board will be up to its full quota after Jan 3, when newly elected Supervisor Don Horsley is also sworn in. Mr. Horsley takes over from former supervisor and now Assemblyman Rich Gordon and will represent District 3, which includes Menlo Park, Atherton, Woodside and Portola Valley.
The all-mail special election, estimated to cost $1.1 million, is the less costly of the two options the supervisors had before them. An election with polling places would have cost the county another $500,000, Mr. Wilson said.
==I Bay City News Service contributed to this report.==