A woman who had sex with identical twins within four days of each other is unable to ensure one of them takes parental responsibility because it is “not possible” to know which is the father, the court of appeal has said.

One of the twins was registered as the father on the birth certificate of the child, referred to as P. His identical twin, along with the mother, sought to take over parental responsibility by asking the court of appeal to overturn a previous family court decision.

Sir Andrew McFarlane, sitting with Lady Justice King and Lord Justice Stuart-Smith, said that while DNA testing has revealed either of the twins could be the father, it cannot distinguish between them so there is a 50% chance of the correct father being already on the birth certificate.

He said the twin on the birth register will no longer have parental responsibility until the court hears further arguments.

The identities of the child, the twins and the mother have been protected by the court.

In a judgment handed down earlier this month, McFarlane said: “Currently the truth of P’s paternity is that their father is one or other of these two identical twins, but it is not possible to say which.

“It is possible, indeed likely, that by the time P reaches maturity it may be possible for science to identify one father and exclude the other twin, but, for the coming time that cannot be done without very significant cost, and so her ‘truth’ is binary and not a single man.”

Judge Madeleine Reardon previously found that “both brothers had had sex” with the woman “within four days of each other in the month when P was conceived”, and that “it is equally likely that each of the brothers is P’s father”.

McFarlane said that the first twin “was not entitled” to be registered as the father and that any parental responsibility he had as a result “shall cease”.

But he said that he was “wholly unpersuaded” to declare this first twin is not the father.

He added: “The failure to prove a fact means that that fact is not proved, it does not mean that the contrary is proved.

“There is a distinction between something being not proven, and making a positive declaration that the fact asserted is not true.”

McFarlane said it was “plainly not in P’s welfare interests for this ambiguity as to parental responsibility to continue.” He added it would be for a lower court to determine “either, both or neither of the twins should now be granted parental responsibility”.