A second man, aged 58, remains in police custody.
Ms Hauser, 18, went missing after she arrived in Larne on a ferry from Scotland on April 6, 1988.
Her body was found two weeks later in a remote part of Ballypatrick Forest, near Ballycastle in Co Antrim.
Police renewed their appeal for information last month – the 30th anniversary of the murder.
Earlier this month senior detectives said they had received the results of further DNA testing which brought their investigation closer to their suspects who murdered and disposed of her body.
Police believe Ms Hauser died shortly after she arrived in Northern Ireland, having been subjected to “a vicious and ruthless assault”.