Police in the United States have arrested a nine-year-old child over the death of a family member who was shot in the head, officials said Tuesday.

Emergency services raced to Tooele, in the Midwestern state of Utah on Friday evening where they found a 32-year-old man who had been grievously wounded.

"He suffered from what appeared to be a gunshot wound to the head," said Officer Colbey Bentley of Tooele City Police Department.

The man, who has not been identified, was rushed to hospital in nearby Salt Lake City but died from his injuries.

"The investigation led to the arrest of a nine-year-old, who is a family member of the 32-year-old male," Bentley told AFP.

The child, who also has not been named, was arrested some time on Friday evening.

"We're looking into a potential charge of homicide," Bentley said.

Firearms claim tens of thousands of lives every year in the United States, a country where there are more guns than people.

Polls repeatedly show a majority of Americans are in favour of stricter rules on ownership, but a powerful gun lobby continues to hold Washington's political class in its grip.