The complainant also has interim name suppression.
Judge James Johnston notes the not guilty pleas and granted the interim suppression order until the man's next appearance in December, when the matter will be fully argued.
He also ordered a mental health report exploring insanity and the defendant's fitness to plead.
According to Rainey Collins Lawyers, bigamy carries a maximum sentence of seven years in prison, and is an offence because it is considered to represent a threat to public morality and to compromise the institution of marriage.
"When a person who is already married marries another person, both parties to the second marriage are committing a crime, irrespective of where in the world the second marriage took place," they said in a post on their website.
"The only defence to the crime of bigamy is if the first spouse has been absent for seven years, and is believed to be dead."