According to a two-page summary of the allegations, Rudd phoned the man in September and threatened to kill him and his daughter.
"This phone call is consistent with a phone call made by the defendant earlier that morning to a business associate in which the defendant spoke about what he wanted done to the first complainant," according to the Crown summary.
Rudd has denied threatening to kill anyone.
The business associate referred to in the summary was originally named in court documents as the intended "hitman" on the charge that was dropped.
He told the Weekend Herald that Rudd offered him $250,000 and "the pick" of any of his expensive cars, but to be his bodyguard - not a payment for what police allege Rudd "wanted done".
Rudd spent at least $9 million on his supercar collection that includes multiple Lamborghinis, Ferraris and Bentleys.
They are housed securely in a hangar at the Mt Maunganui airfield.
The man said Rudd was a "good fella" and the matter had been blown out of proportion as the famous drummer might have been letting off "hot air". However, the Mt Maunganui man, whose young daughter was also threatened, took the alleged threat seriously enough to lay a complaint with the police.
He declined to comment this week: "I have to think of my family and that will always come first".
Another man, named as second intended target in the withdrawn charge, is likely to be called as a witness in the prosecution on the threatening to kill charge.
Suppressions protect the identity of all three men.
Rudd remains on bail at his waterfront mansion - two separate titles he bought for a total of $4.9 million - with windows blacked out by posters promoting his solo album, and security guards posted out front.
He is due back in the Tauranga District Court in February for a case review hearing on the threatening to kill charge, as well as possession of 130 grams of cannabis and 0.7g of methamphetamine.
Rudd plans to deny the criminal offences and the case is likely to be heard in a judge-alone trial.
