Justice Minister Simon Power says he is unable to order an investigation into the murders of Jeannette and Harvey Crewe, and that it is a matter for the police.
Arthur Allan Thomas was convicted twice of the 1970 murders and later pardoned. No-one else was tried and the case remains unsolved
Earlier this year the Crewes' daughter, Rochelle, wrote to the Prime Minister asking for an inquiry.
Mr Thomas' son-in-law, William Rowe, also wrote to Simon Power asking for the same thing.
A spokesperson for Mr Power says the minister has sent a reply saying an inquiry is a matter for the police to decide on.
The police announced last month that they were reviewing the homicide case files.
