'Prolonging life'
Mr Welby is confined to bed, is fed through a tube and speaks through a computer that reads his eye movements.
He appealed to President Giorgio Napolitano in October for euthanasia to be legalised so that he could then request it.
He wants his artificial respirator turned off and to be given sedatives to ease his pain until he dies.
The case hinges on whether Mr Welby is being forcibly administered life-sustaining medical treatment - which is against Italy's constitution.
Prosecutors told the court on Monday that Mr Welby had the right to have the respirator turned off, but that doctors also had the right to turn the machine back on if he was suffering.
"The problem in this case is to know if we are really faced with a case of prolonging life by artificial means," Javier Lozano Barragan, president of the Vatican's pontifical health council, told La Repubblica newspaper.
Prime Minister Romano Prodi's centre-left government is divided over the issue. His coalition includes Catholics as well as socialists, who have come out strongly in favour of Mr Welby's right to refuse treatment.
The centre-right opposition is against switching off Mr Welby's respirator.
Euthanasia and doctor-assisted suicide have been legalised in the Netherlands, Belgium, Switzerland, but remain illegal in much of the rest of the world.