The trio were arrested when they came to buy liquor at a shop, said a senior police officer.
The alleged incident occurred on the Airport Road in Delhi on January 11 when police personnel tried to stop a car during routine check-up when the three occupants of the vehicle allegedly opened fire and fled.
It is not known whether anybody was injured in the incident.
"The trio are identified as Vipin Dagar (24), Praveen Dagar (23) and Ajay Kumar Ahlawat (22)," Superintendent of Police (North) Chandran Chaudhury said.
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Chaudhury said a team of Calangute police led by Police Inspector Jivba Dalvi arrested the trio near the beach.
"After opening fire on police constables in Delhi, the trio had abandoned the car in the national capital and travelled to Goa on the same day," Chaudhury said.
A case under Arms Act and various sections of the IPC was registered against them at Delhi Cantonment Police Station.
The SP said Delhi Police traced the location of the trio after they swiped an ATM card at a hotel and at a shopping centre in Calangute area.
Chaudhury said the police inspector arrested the trio at a gun point as it was suspected that they were carrying firearms.
"One of the accused, Praveen Dagar has cases registered against him in Leh police station in Jammu and Kashmir. He was earlier arrested by the Special Task Force of Uttarakhand," the SP said.
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