Prosecutors say Mason Jordan, while serving as a Honolulu police officer, impersonated young people on social media to lure children to work as prostitutes.
Chief Todd Raybuck was suspended for creating a hostile work environment but an investigation found his hiring practices had been fair.
The officers are on restricted duty but have not been charged, police said. Medical records say police pulled him off a motorcycle or bike.
The board is seeking public comment on the applicants by Monday.
The officers, who were fired this month by the Honolulu Police Department, are also facing criminal charges.
Civil rights advocates say that expanding the board with more police appointments will diminish input from community members.
A House bill would allow state law enforcement agencies to have more information on potential new hires.
His mother says Brandan Maroney was likely in distress when police confronted him and a mental health professional could have helped deescalate the situation.
In all, 37 officers had disciplinary actions finalized last year and another 31 had grievances pending or in arbitration, according to a legislative report.
Attorneys say their client was mistaken by police for a suspect who had already been shot nearby.