BBC director-general Lord Hall gave "specific assurances" about presenter Chris Evans after allegations of bullying were made against him, the chairman of the BBC Trust has said.
Evans stood down from hosting Top Gear on Monday after the show experienced plummeting ratings.
Rona Fairhead told MPs on the Culture, Media and Sport Committee: "There were allegations about bullying at the BBC, and obviously it's an operational matter.
"I have regular discussions with the director-general and he gave me specific assurances (there was) no unprofessional behaviour, he was satisfied with that. As far as any other allegations, I feel it would be inappropriate for me to talk about another member of staff."
Ms Fairhead said she is "absolutely clear" the BBC has processes to deal with the allegations and added there is "absolutely clarity" that the BBC will be a place "where people feel free to raise their hand and it gets properly looked at".
Evans faced a barrage of negative headlines during his tenure as host of the motoring show. He continues to present the breakfast show on BBC Radio Two.
Ms Fairhead denied accusations that she "lobbied" the Prime Minister to be named chairman of the new unitary board that will govern the BBC and that she was "shoehorned" into the role.
She said she was asked to remain in post until the end of her term in 2018 by the Secretary of State and the Prime Minister, but said she did not campaign for the role.
As she was questioned about the White Paper on the future of the BBC and her role on the unitary board, MP John Nicolson said there had "been a great deal of controversy about the way the appointment was made".
He said he understood the Cabinet Office public appointments team and the Cabinet Secretary had complained to the Prime Minister about the way she was appointed because they believed it broke the rules of due process.
Ms Fairhead said she had gone through a "very open, very full and very robust" process before she was named chairwoman of the BBC Trust.
She said Mr Nicolson's comments were a "total overstatement" of what she had said and added: "I had a meeting with the Prime Minister, I did not lobby him for the role."
Ms Fairhead told MPs she hopes to have a "constructive relationship" with Ofcom when the watchdog takes over regulation of the BBC from the trust.
She said she would rather have had a "bespoke" regulator for the corporation, adding: "I'm sure they will come to decisions we are not happy with but I'm not seeing any red lights at the moment."
However, she cast doubt on whether Ofcom would be ready to take over on schedule: "The team at the BBC, DCMS and Ofcom are working flat out to do it as quickly as possible. We are aiming for December but it's very tight."