More than 13,000 rape evidence kits have gone untested or unprocessed in Florida, and clearing the backlog could cost the state tens of millions of dollars, according to study results released Monday.

The study, conducted by the Florida Department of Law Enforcement from August to December 2015, found that 13,435 sexual assault evidence kits across the state have not been tested (PDF). That means that forensic evidence was collected from possible rape victims but has not been processed in order to match DNA evidence with possible suspects.

Authorities said in the report that 9,484 of those tests should have been processed. The state’s law enforcement agency recommends testing all kits “in the interest of public safety.”

The most common reason the kits weren’t tested — cited for 41 percent of the untested kits — was that the alleged victim decided not to proceed with the investigation, according to the report, which surveyed 279 local law enforcement agencies responsible for districts accounting for 89 percent of Florida’s population. In 31 percent of the kits, the state attorney’s office declined to prosecute. Other reasons included a suspect’s guilty plea, an alleged victim’s death or an alleged victim who declined to file a police report.

The report said that the state has been processing an average of about 2,400 sexual assault evidence kits per year in the last five years but that the volume is expected to grow by an estimated 3,500 kits per year.

Backlogs of untested rape kits have been an issue across the United States. In September federal officials said an estimated 70,000 kits sitting in laboratories and evidence collection rooms across the country would be tested with $79 million in federal and New York City funds. Detroit reported in 2014 that it had 10,995 untested kits collected from 1993 to 2006, according to U.S. Department of Justice documents.

There are 12,000 untested kits in Memphis, Tennessee, and 4,000 in Cleveland, according to statistics gathered by the Rape Kit Action Project, a collaboration between the National Center for Victims of Crime, the advocacy group Natasha’s Justice Project and the Rape Abuse Incest National Network (RAINN).

In New York City, which accumulated a 17,000-case backlog from 2000 to 2003, processing the kits and completing DNA matches to suspects resulted in 200 prosecutions, according to the city district attorney’s office. The arrest rate for rapes in the city, which now tests every rape kit for DNA evidence, jumped to 70 percent in 2003, from 40 percent in 2000, after the policy was adopted. That’s compared with a national average arrest rate for rapes of about 1 in 4, according to RAINN.

Experts say it costs $1,200 to $1,500 to complete tests on each kit. The Florida report said any proposals to test the thousands of kits “are dependent upon additional funding for outsourcing, technology, overtime and a stabilized workforce of crime laboratory analysts.”

Florida Gov. Rick Scott announced in November that he will seek $8.5 million to help process the backlog. But that may not be enough; estimates for the funding required to test all the kits range from about $9 million to $32 million over three to nine years, according to the report.

Florida Attorney General Pam Bondi said in a press release that she is “troubled” by the report. “While it is clear it will take more resources to address these problems, testing these unprocessed kits is a public safety issue that deserves our immediate attention,” she said. “Processing these untested kits will allow key DNA evidence to be entered into state and federal crime databases. These entries can produce matches that could link criminals to unsolved crimes in Florida and beyond.”

Three states — Colorado, Illinois and Texas — have passed laws that mandate statewide accounting of untested kits.

Al Jazeera and The Associated Press