The Whitman camp also wants Brown to identify the aide who called Whitman a "whore."
The comment was recorded on the voicemail of the Los Angeles Police Union after Brown failed to hang up the phone.
Brown and Whitman were competing for the union's endorsement.
Brown's campaign issued a public apology for the remark, but Whitman's' camp wants more.
A spokesperson for Whitman issued a statement saying, "After spending months avoiding his 40 year political record, now Jerry Brown is continuing to insult the voters of California by avoiding taking responsibility for his own actions and the actions of his campaign staff."