An inquest into the death of a Tasmanian man who was shot by police is underway in Launceston.

Nicholas Whiteley, 21, was fatally shot by a senior constable at his home at Westbury in November 2010.

Neighbours said they heard a loud argument between Mr Whiteley and his girlfriend, Sheena Button, about 2.00am, and that Ms Button had left a short time later with the couple's baby.

But Ms Button later told the ABC there had been no argument the day Mr Whitely was shot.

Police said Ms Button had contacted them and asked an officer to meet her at the home so she could retrieve property.

The 57-year-old senior constable had entered the home before Ms Button arrived.

Police say he twice called for back-up and used capsicum spray before firing his gun.

The inquest is expected to run for five days.