BURLINGTON, Wash. — A man who led officers on a chase after a bank robbery and was involved in an exchange of gunfire with a Mount Vernon police officer has died — of self-inflicted gunshot wounds, the Skagit County sheriff’s office said Wednesday.

Sheriff’s Chief Criminal Deputy Will Reichardt said 51-year-old William Allen Chapman of Mount Vernon died Tuesday night at Harborview Medical Center in Seattle. An autopsy performed by the King County medical examiner’s office shows Chapman died of two self-inflicted gunshot wounds to the head, Reichardt added.

The man was armed with a .22 caliber pistol and one .22 caliber bullet was recovered from his head. The deputy said the other round appeared to have passed through the skull.

The officer involved in the gunfire exchange after the robbery earlier Tuesday was armed with a .40 caliber pistol.

Reichardt said Chapman and Mount Vernon Officer Tom Wenzel exchanged fire, both firing several shots. Wenzel was not injured; he is on administrative leave.

The sheriff’s office said a civilian witness described seeing Chapman holding a pistol near his own head just before he fell to the ground.