Police say a woman died from a single gunshot wound to her chest. A man was in extremely critical condition with a gunshot wound to his forehead.
Police say a .380 caliber Remington handgun was recovered near the man.
The man was flown to the University of Utah Hospital in extremely serious condition.
Witnesses told police the couple was in a pavilion.
"The two adults were seen in the pavilion talking, walked out of the pavilion didn't seem to be a dispute, weren't arguing, weren't yelling. They heard the shots didn't actually see it," said Lieutenant Rob Hansen of the South Jordan Police Department.
They got up and walked toward their late model Chevy Avalanche before the shots were fired. The couple did not appear to be arguing.
Hansen says the couple is from Riverton and is between the ages of 45 and 50 years old.
Police will release the name of the man and woman after their families are contacted.