The Manhattan district attorney, Cyrus R. Vance Jr., an advocate for expanding the database, wrote in a recent opinion article that taking DNA samples from those convicted of low-level crimes had proved to be effective. He said that since the state allowed prosecutors to collect DNA from individuals convicted of petty larceny, investigators had been able to identify people linked to 48 murders and 220 sexual assaults statewide.

In one case prosecuted by Mr. Vance’s office, DNA from the butt of a cigarette smoked by Lerio Guerrero while he was being questioned for trespassing in Brooklyn last year linked him to a 1998 rape. Mr. Guerrero had been arrested several times in the interim, but none of his convictions were for crimes serious enough to warrant that he give a DNA sample.

Prosecutors also argue that the database could be used to exonerate the wrongfully convicted by matching DNA in their cases to someone else. But the defense bar has argued that courts sometimes place onerous restrictions on gaining access to evidence after a conviction and has, therefore, urged the Legislature to make it easier for defense lawyers to get evidence and run tests against the database.

“New York has a demonstrated problem with eyewitness misidentification and false confessions leading to wrongful convictions,” said Stephen Saloom, the policy director of the Innocence Project. “Any legislation that ignores the recommendations of those who’ve studied these issues is ignoring the heart of wrongful conviction reform needed in New York State.”

The Assembly speaker, Sheldon Silver, a Manhattan Democrat, has pushed to allow defendants access to the database. “We need to see fairness in terms of discovery, in terms of a defendant or a, quote-unquote, wrongfully convicted person,” he said.

The Senate majority leader, Dean G. Skelos, a Long Island Republican, said he was not opposed to access provisions, as long as it was “done in a very tight and controlled way.” Senator Skelos did say he was against including broader so-called wrongful conviction protections in the bill, like videotaping interrogations.

Some in the Assembly, led by Hakeem Jeffries of Brooklyn, have been pushing to include as part of the DNA bill a measure that would make it a violation, rather than a crime, to possess very small amounts of marijuana in public view, but it was not clear whether that provision would make it into the final language.