She alleged the first incident happened in 1997 when she rejected his offer to stay in his hotel room in Washington and have sex.
A year later she said that while he was driving on a Michigan motorway, his hand was “trying to feel me up” by touching her leg and tickling her neck, which caused him to drive erratically.
“I was saved by the bell because we got pulled over by the police for the way he was driving,” she told the Detroit News.
In the last alleged incident, which Ms Maher said happened at a meeting in 1999, the congressman “put his hand up my dress and whispered in my ear, ‘I didn’t know you had such great legs'”.
She told the newspaper she did not quit because she needed the job.
“John Conyers is a powerful man in Washington, and nobody wanted to cross him”, she told the Detroit News.
His lawyer, Arnold Reed, denied the latest allegation, telling the BBC in a telephone interview: “Congressman Conyers is looking forward to the process taking its course and has maintained that he is not guilty.
“He has not acknowledged any wrongdoing on his part.
“The accuser or accusers have the right to say what they feel has transpired from their perspective.
“Mr Conyers equally has a right to maintain that he has not harassed, sexually or otherwise, anyone.”
The BBC also contacted Mr Conyers’ congressional office, but did not receive an immediate response.