Congress is poised to approve $41 million sought by the Obama administration to examine untested DNA evidence collected from rape victims and held by state and local police across the country.

No firm count exists, but recent discoveries in New York City, Los Angeles, Dallas and Detroit suggest that the nationwide total of untested kits never sent to laboratories and kept in police storage exceeds 100,000 — some of them held for decades. Victims usually are unaware that their kits have not been tested, and members of both parties have called the backlogs a national scandal.

On Tuesday, the full Senate is set to take up the funding as part of a $51.2 billion 2015 budget bill for the Justice Department and other agencies that is expected to win floor approval. The House voted May 30 for a budget bill with the funding.

“Whether sexual-assault kits are sitting in crime labs or police lockers, victims deserve to know they haven’t been forgotten,” said Senate Appropriations Committee Chairwoman Barbara A. Mikulski (D-Md.). “The evidence needs to be processed, the case investigated, the criminals brought to justice, and victims provided the services they need.”

The votes come as cities are discovering caches of untested kits and as concern has grown in some quarters over how the Justice Department has allocated more than $1.2 billion since 2004 for programs to expand DNA testing at crime labs. While officials said the funding was aimed at clearing rape-kit backlogs, which have become a symbol of problems in the handling of sexual-assault cases, much of the money has gone toward broader purposes.

While the problem of untested evidence kits in crime labs has been known, the discovery of kits never submitted to labs has reenergized advocates, who say the new grants would specifically target rape kits and help local authorities prioritize and reform the investigation and prosecution of sex crimes overall.

Police may choose to not test evidence in alleged sex assaults if they think it will not be helpful, such as in cases where a suspect’s identity is not in question, an accuser recants or investigators determine a crime did not occur. But in some cases the reason authorities do not submit evidence for DNA testing is that a suspect has not been identified or a prosecutor has not asked, and many departments lack procedures to collect, process and store forensic evidence, according to a 2011 Justice Department report.

Nevertheless, untested evidence may hold powerful clues, especially in “stranger rapes,” because sex offenders are often repeat offenders.

In 2009, authorities found more than 11,000 unprocessed kits at the Detroit crime lab after it was closed for improperly handling weapons evidence. After testing the first 2,000 kits, authorities identified 127 serial rapists and made 473 matches overall to known convicts or arrestees, or to unknown people whose genetic material was found at crime scenes.

The matches came from Michigan, 23 other states and the District of Columbia. Eight men have been convicted and sentenced to prison, 61 others have been charged and await trial, and 150 investigations remain open, according to prosecutors in Wayne County, Mich.

Since 2010, Memphis has found 12,000 untested kits, some dating to the 1970s. Even when the Tennessee Bureau of Investigation received $3.4 million in federal aid to test DNA evidence in cold-case violent crimes in 2003, records indicate it spent only $537,000 of it on a few hundred cases, because of poor planning and limited police participation, the Memphis Commercial Appeal reported.

The New York-based Joyful Heart Foundation, a nonprofit advocacy group for survivors of rape, domestic violence and child abuse, pushed for the new grant program and is seeking police records to determine the scope of the problem in 15 large U.S. cities, including Baltimore, Philadelphia, Tulsa, Miami, Seattle and Las Vegas.

Authorities in the District, Maryland and Virginia have generally not reported large backlogs in police storage, but which kits are counted as backlogged is unclear. Virginia this year enacted legislation calling on the state to inventory untested rape kits held by police and for kits to be submitted for testing by Jan. 1.

According to U.S. Senate appropriators, the new grants would pay to coordinate teams to test, investigate and prosecute sexual-assault crimes. Funds also could be used to train officers, improve law enforcement response to sex crimes and improve services for victims.

Sarah Tofte, a vice president for the Joyful Heart Foundation, said the aid will help offset costs for local authorities willing to tackle the problem.

Dedicated funding “is a relief to public officials” who have committed “to pursue every lead from testing rape kits, reform their criminal justice response to rape, engage survivors in the process and bring offenders to justice,” Tofte said.

While congressional leaders have decried the backlogs, some have questioned why the problem persists.

In debating whether to reauthorize the Violence Against Women Act last year, Sen. Tom Coburn (R-Okla.) complained that under both parties the Justice Department had spent nearly $4 billion a year on more than 250 grant programs, many of which overlap, are ineffective and are poorly managed, he said.

Congress’s main effort in the area, the $1.5 billion Debbie Smith DNA Backlog Grant Program, began in 2004 and was billed as targeting rape-kit backlogs at crime labs. However, its funds can also be used to expand DNA testing for other crimes and to pay for other forensic science programs if authorities say they have no backlog.

The Government Accountability Office, Congress’s audit arm, reported last summer that even though Congress appropriated $691 million from 2008 to 2012 for the program, the Justice Department awarded grants without clearly verifying how the money was spent and could not determine whether backlogs had been measurably reduced.

Justice Department officials say backlogs persist because the country has been expanding the collection of DNA evidence faster than lab capacity has grown.

Nevertheless, nearly half of Debbie Smith funding has gone to purposes other than expanding crime labs and reducing DNA backlogs, including research, training and administrative costs, according to the Rape, Abuse & Incest National Network (RAINN), described as the nation’s largest anti-sexual-assault organization.

Congress last year required that 75 percent of Debbie Smith funding be devoted to DNA testing and allowed money to go to audit rape-kit backlogs.

RAINN and the National Center for Victims of Crime, which calls itself the leading advocacy organization for crime victims, did not initially sign on to the push for the new grants, saying they were concerned that it might siphon funding from the bigger program.

With that ruled out, “we’re pleased to see more resources going towards solving more cases. . . . Having all this evidence and not testing it just increases the number of crimes,” RAINN President Scott Berkowitz said. “It is dangerous for the community and bad public policy.”

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