A 2-year-old boy is recovering at a Utah hospital after being hit in the head by a stray bullet while playing with other children outside in the fenced area of a day care, police said.

Police have identified a man who was shooting birds with a .22 caliber air rifle in an area west of the day care, which is located in Spanish Fork. The man is cooperating with investigators and will be identified only if formal charges against him are filed, according to the Spanish Fork Police Department.

On Monday, several children were playing "in the vinyl fenced area" staffed by two adults when a child "appeared to stumble and was seen bleeding from the face," police said. The day care notified the parents who then brought their child to the hospital for treatment, police said.

"Detectives are continuing to investigate where the bullet may have been shot from and why," Spanish Fork police said in a statement Tuesday. "It appears this was a tragic accident. Open fields are directly west of the daycare and it is believed the round may have come from that area."

At the hospital, doctors discovered a small caliber bullet lodged in the toddler's head and he was then transferred to Primary Children's Hospital where he's currently in stable condition and improving, according to a Wednesday update from police.

When the investigation is completed, the case will be handed over to Spanish Fork city prosecutors for review of any charges, police said.

"I still feel like I'm in shock," said Lane Mugleston, who owns the day care with his wife, told CNN affiliate KSLTV. "We are absolutely surprised. We are dumbfounded that this would happen in Spanish Fork."

Mugleston told KSLTV that at first, the staff didn't think the child was injured by a stray bullet.

"Initially, we thought he just had tripped and hit his head," he said.