Specially-trained officers were called to Downview Road, Worthing, at 10.30am.
Police had reports stating the boy had phoned the NHS 111 service to say he had a gun to his head and deployed the firearms team to arrest him.
A police spokesman said: “Police were called to a report of a youth having phoned NHS 111 stating he was holding a gun to his head at his home in Downview Road, Worthing, on Sunday at 10.30am.
“Firearms officers were sent to the scene but the teenager told the NHS phone operator that he would shoot police who turned up.
“Officers spoke to him outside the property and he came outside.”
The spokesman confirmed a 17-year-old boy was arrested for making threats to kill police officers.
No one was hurt in the incident and no gun was found.
He has been released on bail until March 18.