By Elizabeth Daley

(Reuters) - A newborn baby was in critical condition on Monday after being shot in the head in western Pennsylvania while lying on his father's lap at home, an incident that appears to have been a hunting accident, prosecutors say.

The infant, identified by local media as Thayne Iverson, was just days old when a stray bullet struck him in the head on Sept. 25 at around 7 p.m., said Dianna Rostis, a spokeswoman for the Indiana County District Attorney's office.

She declined to confirm the infant's name or identify the father.

Rostis said an investigation was underway, but it appears that two men were "red-tag hunting" for deer on a neighboring property when a stray bullet entered a window of the home, seriously wounding the baby and grazing his father.

Red-tag hunting allows authorized hunters to kill deer on certain properties to protect agriculture, Rostis explained.

The bullet entered the child's head from the back and exited through his eye socket. The child was airlifted to Children's Hospital of Pittsburgh where he remains, according to Rostis. Local media reports say the baby has been blinded.

Rostis said no charges have been filed against the hunters, but the Pennsylvania Game Commission and the Pennsylvania State Police are continuing to investigate.

(Reporting by Elizabeth Daley in Pittsburgh; Editing by Eric Walsh)