MINNEAPOLIS — The Duluth Police Department and the Anoka County Sheriff’s Office are among the Minnesota law agencies storing the most untested rape kits, the state Bureau of Criminal Apprehension said Thursday.

The Duluth Police Department topped the list, with 578 kits that contain evidence on the shelf,

That’s about 17 percent of the 3,482 unprocessed sexual assault evidence kits reported by 171 law enforcement agencies across Minnesota.

The Anoka County Sheriff’s Office was second, with 495 kits in storage, followed by the St. Cloud Police Department with 306. The Minneapolis Police Department said it had 194 kits in storage, and the Rochester Police Department reported 145. Many of Minnesota’s law enforcement agencies reported having no untested kits. But 25 did not respond.

Minnesota lawmakers directed the BCA last spring to find out how many unprocessed kits are sitting at law enforcement agencies and why they weren’t analyzed for DNA. The primary reason was that the victim didn’t want to pursue charges. Second was a category labeled “other.”

With the Albert Lea Police Department, there were seven untested rape kits since 2005, and with the Freeborn County Sheriff’s Office there was one.

While the Minnesota law calling for the inventory did not mandate more testing of rape kits, agencies have stepped up their efforts.

Kristen Houlton Sukura, executive director of the nonprofit Sexual Violence Center in Minneapolis, said she’s concerned that the kits collected from those who don’t want to pursue charges will be tested, which she said would be a “violation of their rights, a privacy issue.” But she praised the state’s new effort to understand the scope of the problem.

“Now we can see that even in Minnesota where we think we do a great job supporting people, even here this is a problem,” Houlton Sukura said.

The crime bureau estimated if it had an additional eight full-time workers, it could test all of the unprocessed kits in about three years — at a cost of $4.4 million.

The number of kits submitted to its laboratory for testing this year has jumped nearly 40 percent, the BCA said. The bureau said that ideally it wants to turn around DNA evidence in 30 days but it’s now taking about two months to process a kit.

The jump in rape kits is slowing the turnaround times for processing other violent crime evidence, the bureau said.