The special election will coincide with the statewide general and referendum election on Nov. 6.
Maine's four political parties -- the Democrats, Green Independents, Libertarians and Republicans -- have to caucus and have their selections to the Secretary of State's Office by September 13.
Candidates who are not affiliated with a party must submit petitions that have the signatures of at least 100 registered voters by the same date.
Write-in candidates must declare their candidacy by Sept. 20.
The elected candidate will serve the remainder of Davis's four-year term, which runs through the end of 2020.
For forms or more information, call the Elections Division of the Secretary of State's Office at 624-8650.