The attorney general urged anyone with information to contact police
Jersey's attorney general has decided there is "insufficient evidence" to bring a prosecution in one of six cases related to an historical abuse inquiry.
A man and a woman were arrested on 24 June but released without charge.
The allegations were not of a sexual nature and not connected to former children's home Haut de la Garenne.
Three cases have resulted in charges; action has yet to be taken on the other two. About 100 people have alleged abuse dating from the 1960s to 1986.
Attorney General William Bailhache said: "The evidential test has not been passed, and it would be simply wrong to bring the prosecution."
The attorney general said: "I realise that this decision will come as a disappointment to the complainants in the case and possibly to others who have made statements to the police or are considering doing so."
He said he was making a statement about the case because of criticism about its handling.
Lenny Harper, the detective who led the historic child abuse inquiry in Jersey, had strongly attacked the island's legal system.
In an exclusive interview with the BBC, Mr Harper, who retired from the States of Jersey Police earlier this month, blamed "inexplicable delays and decisions" by the States of Jersey lawyers for some cases failing to reach court.
Mr Bailhache responded, saying: "I am obviously aware that assertions have been made, without any basis or foundation, that justice will not be done in the child abuse investigations that are taking place.
"Indeed, it is for that reason that I am making this full statement as to why a decision not to prosecute has been taken in this case."
He added that he wanted "all those who have any relevant evidence to give in the current child abuse investigation to contact the police and to make statements".
"That is the only way the prosecution will be able to reach a fully informed decision on the evidential test in the various cases that come before us for consideration."
Three people have been charged in connection with the inquiry, although more arrests have been made since the last person was charged in May.
There are more than 80 suspects in the inquiry, which is focused on the Haut de la Garenne former children's home.
Jersey Police started an exploratory search of Haut de la Garenne and made their first significant discovery in February, finding what they believed to be a skull fragment.
So far police have found 65 milk teeth and more than 100 bone fragments at the former home.