Michael Martin was aged 26 when he allegedly attempted to rape Jessie Grace Lauder in 1981 at her Newport home in Melbourne's southwest.
He's accused of returning two years later in 1983 and raping her again.
Martin, now 69, made the application for bail after being charged last week with offences including attempted aggravated rape, aggravated burglary, rape and common assault.
He looked forward with his hand over his mouth as Magistrate Belinda Wallington handed down her bail decision on Thursday morning.
Ms Wallington said the alleged offending was extremely serious but she could not find Martin was an unacceptable risk to the community.
Martin grew up about 45 metres across the road from Ms Lauder's home and then moved about 200 metres away when he was married, sexual crimes squad Detective Richard Kelly told the court earlier this week.
It's alleged in September 1981, Ms Lauder heard a loud bang at the back of her home and then saw Martin standing with a knife at her bedroom door.
Martin was wearing gloves, had a pair of underwear over his head and told Ms Lauder to pay him $10 for sex before he tried to rape her, the detective said.
Martin allegedly told her "you won't call police will you" as he left over the back fence, Det Kelly said.
The second alleged sex attack happened in July 1983, when the detective said Ms Lauder heard a smash of glass from the front of the house before she was confronted by a man.
Det Kelly alleged Martin raped Ms Lauder and then said: "Don't tell the police and papers like you did last time."
DNA evidence from the two alleged sex attacks was preserved by police forensics until advancements were made to DNA testing, the detective said.
In 2022, he said the samples were tested and a familial match was found, which led them to Martin.
He was not arrested and charged over the incidents until January 24, which Det Kelly said was due to delays in comparing Martin's DNA with the sample.
Martin is due to return to Melbourne Magistrates Court in April.
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