ALBANY – Lawmakers last night reached deals on a trio of contentious policy issues, agreeing to a major expansion of the state’s criminal DNA databank, an elimination of the statute of limitations for rapes and other felony sex crimes, and the establishment of a Medicaid inspector general to go after fraud, legislative sources said.

Coming just days before the end of session, the compromise marked a turnaround for Assembly Democrats, who had long resisted some of the criminal justice measures they are now apparently backing.

Governor Pataki is expected to sign into law all three pieces of legislation. “We are pleased that both Houses of the Legislature came to an agreement on these three critical items that will help improve the lives of New Yorkers,” Mr. Pataki said in a statement.

The agreement on the Medicaid inspector general carries significance beyond the targeting of fraud and waste in the health system.

Lawmakers expect to save hundreds of millions dollars by monitoring Medicaid more aggressively. The savings allow Mr. Pataki, who has said he won’t support any legislation that increases out-year gaps, to release hundreds of millions of dollars in Medicaid spending on hospitals and nursing homes that he has tied up for legal reasons.

In all three pieces, lawmakers in both houses found middle ground. Senate Republicans have long pushed to abolish the statute of limitations for serious sex crimes, but faced resistance from Assembly Democrats, who only would support such a measure if it also removed restrictions on civil cases.

The deal would eliminate the statute of limitations for rape and other Class B felony sex crimes and would extend the amount of time given to file civil suits to five years from one, a legislative source said.

Republicans and Mr. Pataki have been pushing for a bill that would require all convicted criminals to submit DNA samples. Democrats, who were uncomfortable with the state collecting so much information from people convicted of lesser crimes, were proposing a scaled-back version that would exclude most misdemeanors from the list of offenses requiring collection. Sources said Democrats agreed to include 17 additional misdemeanors in the bill, including petty larceny.

In a win for Democrats, lawmakers agreed not to set a term for the Medicaid inspector general, meaning the next governor will be able to pick a new leader. But the Democrats also dropped their demand for a False Claims Act.