The shooting at 8pm last Saturday at Cherrywood Business Park, south Dublin, followed a massive operation to track down Hennessy and the woman he had abducted, Jastine Valdez.
At that stage, gardaí did not know where the 24-year-old student was and believed she could have been in Hennessy’s car.
There are reports that a 999 call to Garda Command and Control said there were two people in the vehicle at the time. A Garda traffic officer and a detective arrived in separate vehicles.
Various reports have circulated about the incident, including that Hennessy had ran, holding a knife, at either the traffic garda or the detective, and was shot.
There had also been reports, less widely circulated, that Hennessy was making stabbing motions in the car and that the detective might have thought or feared he was stabbing Ms Valdez.
On Wednesday night, Gsoc issued an unusually detailed statement, possibly due to media reports and social media commentary, stating that Hennessy was “in the driver’s seat at the time of the shooting”.
It said one shot had been fired. It confirmed there were also self-harming wounds and a Stanley knife was found in the car.
The body of Ms Valdez was discovered the following day in the Rathmichael area, having been strangled to death.
The Gsoc statement said that following a preliminary examination under Section 91 of the Garda Síochána Act 2005 it was undertaking an investigation under Section 98, “which is for incidents that appear to involve offences”.
Various sources said that while this was a criminal investigation, it did not reflect any judgment that a crime had been committed, only that “potentially” it might.
Sources said Gsoc has an obligation under Article 2 of the European Convention of Human Rights to ensure that “loss of life was justified in all the circumstances”.
One source knowledgeable with Gsoc procedures said: “The garda will have to explain that he had an honestly-held belief that his or someone else’s life was in immediate danger.
“The decision to pull the trigger is an individual one for a garda and Gsoc officers will try and understand his mindset and assess was his view justified.”
The source said investigators were experienced and would be aware that this is “traumatic” for the garda. This source said the witness statement of the traffic garda and any other witnesses present will be “crucial”.
The source added that Gsoc would not have “rushed” into designating it a Section 98 investigation and would have born in mind the Clarke Report of 2016.
Gsoc also have the footage of the ANPR camera in the traffic car, which will have visual imagery and could have recorded sound also, if it was switched on.
A number of Garda sources said these are “split-second” decisions and that if the detective believed Hennessy could have been stabbing Ms Valdez, then he was entitled to use force to stop him. One source cited reports of a 999 call that there were two people in the car.