NEW GERMANY, N.S. - A woman has died after being shot in the parking lot of a grocery store in southwestern Nova Scotia, the RCMP said Thursday.

Police identified the woman as Christina Mae Eisnor, 43, of Hemford, N.S. They said Eisnor died late Wednesday in a Halifax hospital.

A man who was also shot outside Barry's Freshmart in New Germany remained in hospital Thursday in critical condition.

RCMP Sgt. Brigdit Leger said investigators believe the man shot the woman before shooting himself.

"The suspect in this matter received a self-inflicted gunshot wound," Leger said in an interview Thursday.

Const. Les Kakonyi said the investigation into the double shooting would be time-consuming and involve interviewing witnesses in the tiny village.

"We have major crime investigators down there who are trying to piece together (what) led up to his real tragic event," he said.

The man and woman were taken by ambulance to South Shore Regional Hospital in Bridgewater after the midday shooting, but then airlifted to Halifax.

Police have said the man and woman were known to each other, but haven't disclosed the nature of their relationship.

A media report said the two were husband and wife but had separated.

"That's obviously going to be part of the investigation, as well, to establish what their relationship was," said Kakonyi.

"That's going to all come out once the investigators get the opportunity to speak with family members, and friends and witnesses."

RCMP have not said whether investigators have spoken with the injured man.