Richards' testimony was part of an investigation into the business' practices after sting videos were released that allegedly showed company executives discussing the sale of fetal tissue.
Chaffetz, who chairs the committee, started off by asking Richards about funds that were sent overseas.
"Do any of these funds go to the Democratic Republic of the Congo?" Chaffetz said early in the back-and-forth.
"Congressman, let me tell you —" Richards said before Chaffetz interrupted her.
"No, no, no. We don't have time for a big narrative," Chaffetz said.
"I'm not going to give you a narrative —" Richards said.
"Yes or no," Chaffetz replied, before Richards gave a more lengthy response.
A few moments later, Chaffetz asked Richards, "In your 2013 tax return, it lists $3.3 million marked as 'investment' in Central America and the Caribbean. I'm just asking you if that investment was an actual investment."
"We don't own anything in those countries. What —" Richards said as she was interrupted by Chaffetz.
"OK," he said. "I have to keep going."
Chaffetz and Richards later squabbled about the difference between the main Planned Parenthood organization and its fundraising arm.
"I just want to make sure you understood my statements as I know that we're talking about federal funds," Richards said. "Zero federal funds are related —"
"It's the co-mingling that bothers us!" Chaffetz replied. "Every dollar —"
"We —" Richards said.
"Now hold on," he said.
There were several instances when Richards attempted to clarify statements Chaffetz made about Planned Parenthood, interjecting with an "excuse me, sir" to which Chaffetz would say, "hold on."
Chaffetz also continued to interrupt Richards' testimony, which was noted by some of his fellow Congress members.
At one point, Rep. Gerry Connolly (D-VA) asked Richards after he asked a few questions, "Is there anything else you want to add, uninterrupted, with some sense of respect, Ms. Richards? Let me at least provide that to you."
Chaffetz also took time to note Richards' salary.
"Your compensation in 2009 was $353,000. Is that correct?" he asked.
"I don't have the figures with me, but —" Richards said.
"It was," Chaffetz replied. "Congratulations."
Watch some of the exchange:
This post has been updated.