But the attorney general says the Legislature should clamp down on the practice and make sure lawmakers are reimbursed by only one entity for travel expenses.
King began investigating in September after KOB-TV reported that Begaye was reimbursed by both the legislature and organizers of an Arizona conference. He later returned $1,800 to the conference.
The Legislature is reviewing travel payments and considering a more restrictive policy.
Begaye lost his re-election bid last week. He did not respond to requests for comment from the Albuquerque Journal ( http://bit.ly/W8DxRb) on Wednesday.