HOOKSETT — State prosecutors confirmed that someone who showed “recent signs of drug abuse” killed a Hooksett couple last Sunday before stealing their car and leading police in Massachusetts on a high-speed chase before he killed himself.

An autopsy performed Thursday determined June Cosma, 79, and her husband, Thomas Cosma, 80, died due to “blunt force trauma to the head.”

Attorney General Gordon J. MacDonald, along with state and local police, said police in Andover, Mass. were involved in a chase Sunday with a car near the Andover-Lawrence line. The car evaded officers and was later found abandoned in Lawrence, Mass.

Zachary Gloudemans, 34, who matched the description of the driver of that car, was found dead a short distance from the car. Police investigators learned the car was registered to the Cosmas.

New Hampshire law enforcement officials went to do a welfare check on the Cosmas at 47 Kimball Drive and found both of them dead, officials said Monday.

The Cosma family issued this statement Thursday: “We are thankful for the support we’ve found the past few days since first learning what might be and then confirming their unfathomable demise. We are grateful for the support, love and concern we have already received through heartfelt words, thoughts, prayers, calls, texts and messages.”

The family also thanked state law enforcement and prosecutors for their “earnestness, professionalism and concern.”

“We face the grim reckoning there is no way justice will be meted out for the reprehensible manner in which the Cosmas’ loving presence was stolen from us,” the statement concluded, asking that the family’s privacy be respected.

The investigation revealed Gloudemans had been staying in a residence near the Cosmas’ home prior to the murders. Those interviewed in the neighborhood told authorities that Gouldemans had showed signs of having abused drugs.

MacDonald said the matter is being investigated as a likely double-murder, followed by a suicide.

The Massachusetts Medical Examiner’s office performed the autopsy on Gloudemans.

New Hampshire Assistant Attorney General John Kennedy said at the time of the incident, Gloudemans was living near the couple.

“Mr. Gloudemans was living at an address in close proximity to the Cosmas. At this point in the investigation we are still withholding exactly where he was living,” Kennedy said.

Since Monday, state officials have stressed there was no threat to the general public, but did not offer any details until Thursday.

The home where the Cosmas lived is on a sparsely populated stretch of a dead-end road, and sits at the base of a heavily wooded hill on the banks of the Merrimack River.

Union Leader Correspondent Travis Morin contributed to this report.