WE have a tool that can prevent hundreds of murders, rapes and robberies each year at minimal cost to taxpayers. But we’re not using it in a majority of cases because a state law restricts its use.

DNA evidence solves crimes. Since 1996, when New York State’s DNA databank opened with strong support from my predecessor, Robert M. Morgenthau, the bank’s DNA samples have been linked to more than 3,500 sexual assaults, 860 murders, 1,100 robberies and 3,400 burglaries. Thousands of criminal convictions have resulted. Today, however, we are hamstrung by a law that does not authorize the collection of DNA following convictions of certain misdemeanors. This has meant that we can’t use DNA technology in more than half of our cases. By expanding the collection of DNA to include those convicted of all crimes in New York State’s penal law, as Gov. Andrew M. Cuomo has called for, we will be better able to identify the guilty, exonerate the innocent, bring justice to crime victims and prevent additional crimes from occurring.

In 2006, lawmakers decided to include some but not all misdemeanors in the DNA databank. Opponents questioned why someone convicted of a low-level misdemeanor — petty larceny, for example — should be required to provide a DNA sample. The answer can be found in the results of that decision: samples collected from people convicted of petty larceny have been linked to roughly 48 murders and 220 sexual assaults. Clearly, the 2006 expansion of the DNA program — which passed with only six dissenting votes in the State Assembly — confirmed that collecting samples from offenders convicted of minor crimes helps solve and prevent more serious crimes.

Whom does DNA bring to justice, and how does it prevent future crimes? The case of Curtis Tucker is instructive. Following his conviction in 2010 for robbing and assaulting a 74-year-old Manhattan man suffering from Parkinson’s disease, Mr. Tucker was required to submit a DNA sample, which typically is obtained by swabbing the inside of a person’s cheek. Three days later, that $30 test produced a match linking Mr. Tucker to a brutal 2004 assault and attempted rape of a 15-year-old girl in the stairwell of her Manhattan apartment building.