"I know the speaker didn't go over a bridge and leave a young person in the water, and then have a press conference the next day," the embattled Connecticut congressman told The Hartford Courant in remarks published Wednesday.
"Dennis Hastert didn't kill anybody," he added.
Shays' comments recalled the 1969 Chappaquiddick incident, when Kennedy's car ran off a Massachusetts bridge, killing his passenger, Mary Jo Kopechne. Kennedy did not immediately report the tragedy and later pleaded guilty to leaving the scene of an accident.
Last week, Kennedy campaigned for Democrat Diane Farrell, who is locked in a bitter fight with Shays that could help determine whether Democrats recapture the House after 12 years of GOP control.
"This is symptomatic of Chris losing his composure in a tight race," Farrell said in a telephone interview with The Associated Press on Wednesday. "Chris just seems to be lashing out in anger."
Farrell said the scandal, which polls show could hurt the GOP's bid to hang onto control, has affected her because her 19-year-old daughter Margaret was a Senate page when she was 16.
"My first reaction to this whole scandal had nothing to do with politics," she said. "It was as a parent who had a child participating in the program."
Shays cited Chappaquiddick in an interview Friday when he was asked about Farrell's call for him to return money raised by Hastert. The speaker has been under fire for his handling of disgraced former Rep. Mark Foley's sexually explicit messages to young pages.
Farrell has called for Shays to return any money raised for him by Hastert. She and other Democrats have called for Hastert to resign.