KALISPELL — Police investigating the shooting of a hospitalized Kalispell infant said they are skeptical the parents are telling the whole story.

Flathead County Undersheriff Pete Wingert said police are still asking a lot of questions, and trying to corroborate evidence back to the witness statements.

Police responded to a report Tuesday afternoon that the 1-year-old baby had been shot with a .22-caliber pistol. The girl was flown, in stable condition, from Kalispell Regional Medical Center to a Spokane hospital later in the evening.

The mother told police that the 1-year-old was left with a 2-year-old girl in a truck, during blustery weather, while the parents piled brush on a piece of property south of Kalispell.

Neither child was buckled in, Wingert said.

The mother said a gun was regularly stored beneath the passenger’s seat, but was kept unloaded. Police are skeptical such a small child could load a gun.

‘‘That’s a lot of fine motor skills for kids that age,’’ Wingert said.

When the mother heard the gunshot, he said, she and her husband rushed to the truck, discovering the infant with a bullet wound that entered near the chin and exited at the left jawbone.