The Lifford man, 46, was detained by appointment in Dublin earlier this month.
However both the Gallagher and Gillespie families in Lifford and the Twins Towns have still not had contact with the Department of Justice.
A spokesman for the Gallagher family told Donegaldaily that THEY are now trying to contact Government officials.
“We heard the rumour yesterday but we still have not received any calls from the Department of Justice or the Gardai for that matter.
“We thought we would have heard if our brother was being detained in a mental institution after what he did and all we have been through.
“We are trying to contact the Department of Justice ourselves now to try and find out some more,” said the spokesperson.
Gallagher, who murdered mother and daughter Anne and Annie Gillespie in the grounds of Sligo Hospital in 1988, was living in Strabane, Co Tyrone.
He killed Anne, 18 and her mother Annie, 51, after learning how Anne planned to dump him.
Gallagher also tried to kill Anne’s uncle Patrick Maguire but the gun jammed when he tried to shoot him.
Gallagher, who was then 22, was tried for murder but was found to be insane.
Twelve years later he escaped from Dundrum Central Mental Hospital and fled to England where he lived for a number of years.
However he returned in 2003 and set up home in Strabane just a few miles from where his victims lived in the Twin Towns of Ballybofey and Stranorlar.