The video, recorded in 2009, showed Mr Rudd becoming increasingly frustrated while filming an address.
Mr Rudd says he is not satisfied with a Federal Police investigation which did not result in charges being laid.
He says documents he obtained under freedom of information laws prove that a crime was committed.
"Their conclusion is that a crime against the Commonwealth Crimes Act has been committed, and this involved the theft of Commonwealth property," Mr Rudd said.
"That's a serious matter and we should get to the bottom of it."
Mr Rudd had written to the Australian Federal Police, suggesting who they should speak with.
"The bottom line is I would just hope that the legal matters associated with this are dealt with as they'd be dealt with for any other Australian citizen," he said today.
"I'm just another Australian citizen when it comes to the theft of property."
The AFP says the matter remains finalised, but officers are interviewing potential witnesses.