A second envelope addressed to the Greens senator Sarah Hanson-Young raised alarm in the Adelaide office of the party.
The delivery led to the evacuation of the headquarters of Greens SA on Tuesday, a day after the first envelope containing dust and a threat was received.
The powder was tested and a dangerous chemical was not found, a police spokesman told AAP.
The staff did not open the second envelope that arrived on Tuesday addressed to Senator Hanson-Young in a similar spelling.
The police also clarified any danger.
The South Australian senator, who was returned to the Saturday election, did not detail what was in the note in the first envelope, but confirmed that it was directed at her.
He labeled the person who sent an "idiot".
"It was a white powder with a serious threat," he told ABC radio on Tuesday.
"Everyone is fine, the staff is okay but, of course, it's not a good thing for those front-line employees who get the mail to deal with.
"Anyone who has done this right, frankly, is an idiot."
Australian Associated Press