The fingerprints found by police have already been linked to a potential suspect, although the investigation is ongoing.
A spokesman for West Yorkshire Police said today: "During the evening of the 1st of April, Lawnswood Cemetery and Crematorium suffered a burglary. "Suspects forced open the wooden door of the premises and once inside stole three books of remembrance from within glass cabinets.
"The books were later recovered within the grounds ripped up and destroyed.
"Forensic examinations have taken place and fingerprints were found and linked to a potential suspect. Enquiries are ongoing."
The books are held at the crematorium so that people can leave messages and memories for lost loved ones after funeral services.
Which books were affected?
The book room is open for the public to leave flowers and light candles for loved ones, but three books have been taken away to be rebuilt.
The books relate to the months of April, May and June. Anyone who has an entry within those months, regardless of the year, will be affected, the council said. It means those books will not be available for viewing.
-> Revealed: The other places in the world named LeedsA spokesman said in a statement: "The months of July through to March have not been damaged. The books all go back to the first half of the last century.
"The damaged books have been taken to a professional restoration and binding company who will systematically work through each damaged page to recover and restore as much of the original information as possible.
"Once the pages are recovered they will be photographed before being rewritten in exactly the same style and format.
"The recovered pages will be also be uploaded in digital format for future viewing by the public.
"We are reviewing how the books are held at this and other sites across Leeds moving forward.
"The vandalism took place between 9pm on Sunday 1st April and 7:30am on Monday 2nd April.
"The vandals gained entry to the book room by forcing the doors of the book room to break in and then gained access to the books by forcing open the locked cabinets in which the books were kept.
"Footage from the CCTV on site is being viewed in detail to see what information can be used to track down those responsible."