Ambulances were diverted during the three-hour lockdown of University Hospital Crosshouse in Kilmarnock, which was lifted shortly before 11pm in Thursday evening
Police were called to the first incident at the East Ayrshire hospital at about 7.45pm
They believe another in the centre of Kilmarnock about 20 minutes later and a serious crash on the A76 may be linked.
The incidents are not being treated as terror-related.
In a statement, Police Scotland said there was no cause for concern for the wider community.
It added that inquiries were at an early stage and that the areas involved have been cordoned off.
The second incident was on Portland Street, which is about two miles from the hospital, at about 8.05pm.
Police have not confirmed the nature of these incidents, however, It’s understood a member of staff has been seriously injured.
Officers were called to the crash on the A76, on the outskirts of the town, at about 8.30pm.
Local residents reported hearing sirens and a helicopter overhead shortly before 8.30pm
Dr Crawford McGuffie, the medical director of NHS Ayrshire and Arran, said police had confirmed the risk to patients, staff and visitors to the hospital was minimal.
He added: “There remains a large police presence on the grounds of the hospital.
“We would like to reassure anyone coming to the hospital, in particular to any patients or staff coming on shift, that Police Scotland have confirmed it is safe to do so.”