More than 13,000 rape kits around the state of Florida have gone untested, the state’s law enforcement agency announced on Monday. The costly backlog may take years to clear.

The report, by the Florida department of law enforcement, estimated that testing may cost the state anywhere from $9m to $32m. The agency will present its full findings to the legislature.

Law enforcement agencies across the country have struggled with their failure to test old rape kits. In July, a USA Today investigation found evidence that more than 70,000 rape kits have gone untested nationally.

In September, federal officials promised to speed up testing. As part of that effort, the Justice Department (DoJ) distributed $41m in grants to help police departments develop procedures for preventing rape kit backlogs.

But those grants are directed at police forces who will spend less than half of the money on testing old rape kits, according to the application guidelines.

The DoJ has also struggled to distribute other money set aside for police departments investigating the extent of their rape kit backlogs for the first time.

In 2013, Congress passed a law that increased spending on forensic analysis that must go toward inventorying and testing rape kits, and set aside grants to help police forces count and process their untested rape kits.

As of July, however, the Justice Department had not distributed any such grants. An audit noting the department’s poor oversight also called into question whether it was capable of ensuring that local police increased their spending on testing rape kits.

Rape kits consist of swabs and other forensic evidence collected from alleged rape victims by trained medical professionals. Evidence must be collected soon after the crime in a process taking several hours.

Testing old rape kits usually leads to a torrent of new prosecutions. Several law enforcement agencies have found that the rape kits point to serial rapists.

After Detroit processed a backlog of 11,000 rape kits, police identified more than 100 serial rape suspects.