Grant Jones, 24, almost blinded the aircraft's crew when he flashed a bright green light into the 'copter's cockpit on October 1 last year.
Edinburgh Sheriff Court heard how the pilot was forced to turn the craft away from the laser in order to avoid his sight being affected by the intense ray.
His colleagues used heat cameras to track Jones who escaped into a house in Silverknowes Crescent, Edinburgh.
They alerted officers on the ground who then tracked Jones down and found a laser pen in his possession before arresting him.
Jones, of Silverknowes Crescent, pleaded guilty to breaching the Civil Aviation Act.
He admitted directing a light so as to dazzle or distract the pilot of an aircraft in flight by pointing a laser pen at a Police Scotland aircraft.
Depute fiscal Isabel Clark told the court the helicopter was helping officers search for a stolen vehicle when Jones put the crew's lives at risk.
Ms Clark added: "One of the police officers became aware of a green laser light coming from Silverknowes Crescent.
"The pilot had to take immediate action in order to avoid danger to his sight or to the sight of the other people on board the helicopter."
Ms Clark told the court that the helicopter pilot had to turn his aircraft around to avoid the bright glare of the laser.
The crew then used heat cameras to track Jones as he tried to make his escape into his house on Silverknowes Crescent.
The Police Scotland helicopter invloved was based at the heliport in Finnieston, Glasgow. It crashed into the Clutha Bar on Friday November 29 2013.
A total of 10 lives were lost in the incident.
Sheriff Nigel Ross deferred sentence on Jones in order for the court to obtain reports.
He will be sentenced on June 2.