New voter registration rule As of Aug. 16, third party voter registration can take place in local county clerk offices, thanks to a new rule passed by Secretary of State Rebecca Vigil-Giron. Third parties may also still register at the Secretary of State’s office The rule applies to voter registration for statewide primary elections, general elections, any special statewide elections, county wide elections, elections to fill vacancies in the office of the U.S. Representative, and regular or special school district elections, according to a release from Vigil-Giron’s office.