A retired NYPD officer was showing off a gun to his Long Island doctor Wednesday morning — and accidentally shot himself and his physician, police sources said.

The 77-year-old patient, who is licensed to carry the firearm, was inside his doctor’s Oceanside office around 10:20 a.m. when he popped off a single bullet that went through his leg and struck his physician in the foot, sources said.

They were both taken to South Nassau Hospital.