A mother and daughter were the victims of the attacks in Kilmarnock that forced a hospital into lockdown.
A man then died in a car crash linked to the women’s deaths in the East Ayrshire town.
Emma Robertson Coupland, 39, was found injured in the car park of University Hospital Crosshouse, near Kilmarnock in East Ayrshire, at around 7.45pm on Thursday but she died at the scene.
In a second incident 20 minutes later on Portland Street, Kilmarnock, her daughter Nicole Anderson, 24, was stabbed.
Emergency services attended the scene and she was taken to the hospital at Crosshouse, but she later died.
Steven Robertson, 40, then died in a car crash on a minor road between the B7036 and the A76 on the outskirts of Kilmarnock, at around 8.30pm.
Police said inquiries so far suggest the incidents are linked and officers are not looking for anyone else as part of their investigation.
Chief Superintendent Faroque Hussain said: “A number of locations remain cordoned off as officers continue to conduct inquiries.
“We are working to confirm the full circumstances of what has happened. If anyone has any information which could assist our inquiries, please do contact us.
“Understandably, people will be shocked by what has happened.
“We are still in the process of establishing the full circumstances, however I would like to reassure people that there is no wider threat to the community.
“Officers will be on patrol and anyone with any concerns can approach these officers.”
The relatives of those involved have been informed.
Heartbroken friends and family members have since paid tribute on social media to Emma and Nicole.
Emma’s daughter and Nicole’s sister posted on Facebook: “Life will never be the same without use [sic].”
Nicole’s fiancee wrote: “I will miss that beautiful smile that wee gorgeous person inside and out you made me the happiest person on this planet daily until we meet again baby, I love you.”
Another relative added: “Honestly can’t even put into words how I’m feeling, absolutely devastated to say the least got the worst news of my life yesterday I just can’t take it in, I’ve lost wee cousin my childhood best friend my wee sister and my saviour all in one.”
A statement on Thursday night from police said the incidents are not being treated as terrorist-related.
The hospital was locked down following the first incident, but that was lifted at around 10.30pm when police declared it safe.
On Friday morning, the hospital’s A&E department and main entrance were open and running as normal while two police vans full of officers remained outside with police tape around part of the car park.
Ahead of the daily Scottish Government coronavirus briefing at Friday lunchtime, Deputy First Minister John Swinney spoke about the “dreadful” events.
He said: “A tragedy like this would be impossible to understand at any time, but after the events of the past year it is particularly shocking that such an incident has taken place at an NHS hospital.
“An investigation is of course ongoing, however Police Scotland have confirmed that the site at Crosshouse Hospital is secure and it is safe for patients and staff to go there.
“For now I simply want to thank the police officers and all of the medical staff who were involved in the response to this incident for all that they contributed and to express my sympathy to the staff of the hospital for the trauma to which they are having to come to terms.
“And again I want to send my deepest condolences to the family and the friends of those who have been killed.”
First Minister Nicola Sturgeon tweeted: “Dreadful news. My thoughts are with the bereaved.
“Thinking too of everyone at Crosshouse Hospital, already dealing with the tough circumstances of Covid. I’m also grateful to our emergency services. Please continue to follow ?@policescotland? advice.”
Several roads in Kilmarnock town centre remain closed – including Portland Street, West George Street and Garden Street via Hill Street – as well as where the crash occurred, with diversions in place.
An East Ayrshire Council statement said: “Following on from the tragic incidents in and around Kilmarnock last night, our thoughts are with all the families and individuals affected by these events.
“We know our communities will be shocked and saddened by these events, but we wish to reassure them that there is no risk to the general public at this time and we are supporting our colleagues in NHS Ayrshire & Arran and Police Scotland wherever we can.
“As this is an ongoing police matter, we need to keep a number of roads in Kilmarnock town centre closed and diversions are in place here, and on the A76, to allow the investigation to continue, and we thank you for your patience and understanding.”