The suspect, Richard Cottingham - believed to be one of America's most prolific serial killers - was arraigned on Wednesday on a second-degree murder charge in connection with Cusick's 1968 killing.
From a hospital bed in New Jersey, where he is already serving a life sentence for other killings, Cottingham pleaded not guilty.
While he has claimed he was responsible for up to 100 homicides, authorities in New York and New Jersey have officially linked him to only a dozen so far, including Cusick.
He has been imprisoned since 1980, when he was arrested after a motel maid heard a woman screaming inside his room.
Authorities found her alive but bound with handcuffs and suffering from bite marks and knife wounds.
"He is a violent predator and no matter how he looks today in a hospital bed he was not always a feeble older man," Nassau County District Attorney Anne Donnelly said in an interview with The Associated Press.
"He was a young 22-year-old when he committed the murder of Ms Cusick. He was strong, stronger than these women were, and he was violent."
Authorities believe Cusick, 23, left her job at a children's dance school and stopped at the Green Acres Mall in Nassau County to buy a pair of shoes when Cottingham followed her out.
Detectives believe he pretended to be a security guard or police officer, accused her of stealing and then overpowered the 44kg Cusick, Nassau County Police Detective Captain Stephen Fitzpatrick said.
She was "brutally beaten, murdered and raped in that car", Fitzpatrick said.
The medical examiner concluded Cusick had been beaten in the face and head and was suffocated until she died.
She had defensive wounds on her hands and police were able to collect DNA evidence at the scene, although at the time there was no testing capability.
Police interviewed dozens of people, retraced her steps and never stopped hunting for her killer. But the trail went cold.
Cottingham was working as a computer programmer for a health insurance company in New York at the time of Cusick's death.
He was convicted of murder in New York and New Jersey in the 1980s, though the law at the time did not require people convicted to submit DNA samples, as it does now.
His DNA was taken and entered into a national database in 2016 when he pleaded guilty to another murder in New Jersey.
In 2021, police in Nassau County received a tip that a suspect who might be responsible for killings in the county, just east of New York City, was locked up in New Jersey. They began running DNA tests again on cold cases and came up with a match to Cottingham.
Prosecutors are now reviewing all open cases around the same time and running DNA to see if Cottingham may have been responsible for other killings.
"Based on evidence that we have in this case, we are reviewing all murders of young females from 1967 to 1980," Donnelly said.
