Best Buy said Monday that former company chief executive Brian Dunn, who resigned his post in April, was engaged in a close relationship with a female employee while he held the top job. The company also alleged that chairman of the board Richard Schulze knew of the relationship, but did not bring it to the attention of the audit committee. Schulze’s successor was announced Monday as well. Best Buy has been taking a closer look at Dunn since he resigned, questioning his conduct and that of executives around him who may have failed to report questionable personal behavior. Last week Reuters reported that company investigators had spoken to a 29-year-old female staffer in connection with the claims of personal misconduct.