The discovery the prints have disappeared has led to a call for a new commission of inquiry.
It comes weeks after the Weekend Herald revealed detectives were interviewing members of the Thomas family in connection with the killings.
"The Crewe Review Team are aware that fingerprint examination holdings from the 1970 homicide investigation cannot be located," a police spokesman said.
"Exhibit handling generally is an important topic area being assessed and will be addressed in detail in the review report."
Police have refused to say whether the report will be released in full.
Des Thomas, brother of Arthur, said the loss of the prints meant it would not be possible to rule out two suspects considered separately to be possible culprits in the killing.
"If they had these prints they could go around there and eliminate them [from the inquiry]."
Mr Thomas said he had been told the fingerprints from inside the Crewes' car, seen driven in the area and outside the house, had also gone missing. "We've got to have a commission of inquiry."
Des Thomas said he believed police had the fingerprints and DNA evidence but were withholding them. He said finding the killer would focus questions on the lack of any criminal inquiry into corrupt policing.
Crewe murder author and researcher Chris Birt said the fingerprints from the house and car could lead police to the killer.
"If key exhibits from what is undoubtedly the most scrutinised double homicide case cannot be kept safe [in police care] then answers must be demanded and explanations given at the highest levels."
Defence lawyer Gary Gottlieb said police needed some form of independent oversight on the Crewe case. The disappearance of key evidence such as fingerprints should not happen, he said. "It is a case of huge public interest ... This is one of the cases where there has been the most concern over police behaviour."
Labour Party justice spokesman Andrew Little said police should have nothing more to do with the Crewe case, which should be independently investigated. "I don't think it is healthy for them and their reputation, or the people whose lives have been blighted by the case."
He said he wanted a body formed to investigate miscarriages of justice - an idea Labour would explore if returned to government.
• Read also: Why the missing Crewe fingerprints are critical, says researcher