The thirty-year-old diplomat died after falling from the seventh floor on the Lower East Side building in the early hours of Wednesday morning.
According to reports, he had suggested playing the game with his long-time friend and brother-in-law, James Waugh, who was said to be upset that Mr Simpson had earlier swung his wife around the rooftop.
Mr Simpson was married to Mr Waugh's sister Lauren.
'I will prove that you can trust me. Let's play the trust game,' Mr Simpson told his brother-in-law as he leaned over his balcony ledge, according to police sources.'
Facing the apartment, Mr Simpson is believed to have sat on the rooftop railing before falling backwards.
Mr Waugh told police he held out his arm to catch the Australian diplomat but lost his grip.
Mr Simpson landed on a second-storey terrace at about 1.30am and was pronounced dead at the scene in what police are describing as a tragic accident.
'He's described as somebody who liked to play games and had sat on the balcony railing and accidentally lost his balance,' NYPD spokesman Martin Brown said.
Mr Simpson had earlier been out with his wife and their friends before they all returned to his apartment to admire the view of the Empire State Building.
The iconic landmark had been lit up in rainbow colours to celebrate Australia's gay marriage vote.