HUD, she said, immediately initiated a review and determined that there was no illegality in his actions.
"There were no illegal acts; there was indiscretion, fraternization, yes," said Jereon Brown, a HUD spokesman who joined Newton Cole in an interview.
In an interview with The Inquirer Tuesday afternoon, Kelly, who is married, called the matter "a lapse of judgment and a personal family failure. I failed my family, my friends, my colleagues."
Kelly was hired Monday as head of housing and community development for the District of Columbia.
The woman in question was a senior PHA manager who recently left the agency. Kelly said the relationship had ended.
"I recognized the wrongness of that long ago," he said.
Kelly was informed of the HUD review results in May and submitted his resignation two weeks ago. The news of his departure was made public last Friday.
The review included an inspection of credit card statements, travel records, schedules, and bonuses, as well as interviews with employees, including Kelly.
When confronted by HUD officials, Kelly acknowledged the "indiscretion," Brown said.
"We explained the circumstances to Michael ... that it was an improper relationship and it would be hard to correct," Brown said.
"It was an improper relationship and it would be hard to correct," he said.
Brown said it would set "a bad example for the rest of PHA."
"This boils down to the workplace environment and proper superior-subordinate relationship," he said.
Kelly was recruited by HUD to take over PHA following the 2010 firing of Carl R. Greene, who was accused of sexually harassing female subordinates and secretly approving settlements with them totaling more than $600,000.
In an interview with The Inquirer on May 30, Kelly shared PHA's new ethics policy. It specifically forbids managers from being romantically involved with subordinates.
Kelly noted that the new rules only took effect Friday. In Tuesday's phone interview, he said, "I was setting a standard that I couldn't hold myself."
"That was the basis for my resignation," he said.
Kelvin Jeremiah, who for 10 months has served as PHA's head of audits and investigations, has replaced Kelly as acting executive director.
Contact staff writer Jennifer Lin at 215-854-5659 or firstname.lastname@example.org, or on Twitter @j_linq.