JACKSON (AP) — Lawmakers sent a bill Friday to Gov. Haley Barbour that would require Mississippi to preserve DNA collected in felony cases — legislation inspired by the exoneration of a man who was cleared in a brutal child killing, in part, because of a blood sample.

The House approved the measure 121-1. It had passed the Senate earlier.

Many law enforcement agencies across the state gather biological, or DNA evidence, during investigations, but the samples aren’t always maintained. Under this bill, that evidence would be preserved, either by the Mississippi State Crime Lab or local law enforcement.

The need for the law was underscored by the 2008 exoneration of Kennedy Brewer, who had been convicted of capital murder in the rape and strangulation of a 3-year-old girl. DNA cleared Brewer in the attack years after he was sent to Mississippi Death Row.

‘‘The fact that the DNA in his case was preserved and testable was sheer luck,’’ said Tucker Carrington, director of the Mississippi Innocence Project, a group that works on behalf of inmates thought to be wrongly convicted.

‘‘You’d have to think that any person in the Legislature would be rattled by the possibility that the state really did come pretty close to executing somebody who was innocent,’’ he said.

Carrington headed a task force created by the Legislature in 2008 to make recommendations about handling DNA evidence. Carrington stressed that the bill does not obligate law enforcement to gather DNA in all cases.

‘‘All it does is say, if you collect DNA in a felony case, then you’ve got to keep it for the length of time the person is locked up,’’ Carrington said.

He said the bill also requires that DNA collected in past homicide and sex offense cases be preserved and it allows for post-conviction testing under certain conditions.

Mississippi is one of six states that doesn’t have a DNA preservation law, Carrington said.

The law would go into effect once Barbour signs the bill, which Rep. Bobby Moak said would give the state enough time to apply for a share of millions of dollars in grants offered by the U.S. Department of Justice. Barbour’s office did not immediately reply to a message asking whether he will sign the bill.

Mississippi wasn’t eligible for much of the approximately $32 million in federal funding that’s available to states because it didn’t have a DNA law, Carrington said.

Sam Howell, director of the state Crime Lab, said he believes the facility he oversees in Jackson is the best place to store the evidence, but ‘‘the vault is at its capacity.’’

Howell said the federal funding cannot be used for brick and mortar projects, such as expanding the state Crime Lab. The agency has been traditionally underfunded in the past, and lawmakers have said in the current economy few agencies would see huge budget increases.

Howell said the federal money could be spent, however, on the cost of outsourcing DNA that might need retesting.

Moak, a Democrat from Bogue Chitto, said he was hopeful the bill would prevent instances of wrongful imprisonment, such as Brewer’s case.

Brewer was convicted and sentenced to death in 1995 in the slaying of Christine Jackson.

According to the New York-based Innocence Project, Justin Albert Johnson of Noxubee County was linked to Christine’s murder in 2001 after the group sent a blood sample — taken soon after the 1992 killing — for DNA testing. Johnson’s DNA allegedly matched semen found on Christine’s body.

The blood sample used in the test had been preserved at the state Crime Lab for years.

Last year, authorities said Johnson allegedly confessed to Christine’s murder, and that of another 3-year-old girl, Courtney Smith.

The evidence and alleged confession also led to the exoneration of Levon Brooks, who had been convicted of murder and sentenced to life in prison for Smith’s murder.

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The bill is Senate Bill 2709.