(CNN) -- A man shot his estranged wife to death, along with their son and grandson, before turning the gun on himself as police closed in, authorities in Livingston Parish, Louisiana, said Sunday.

Police say Dennis Carter Sr. shot four family members, three fatally, before turning the gun on himself.

Dennis Carter Sr., 50, also shot and critically injured his pregnant daughter-in-law, the parish sheriff's office said in a statement. The shootings occurred Saturday night in the town of Holden, Louisiana.

Authorities were dispatched to a report of shots fired at a home about 10:40 p.m. Upon arrival, they found three people dead and the fourth -- Amber Carter, 25 -- in critical condition, the statement said.

Those killed were Dennis Carter Jr., 26, Amber Carter's husband; their son Mason Carter, 2; and 49-year-old Donna Carter, mother of Dennis Carter Jr. and estranged wife of Dennis Carter Sr., police said. All had been shot to death. A 16-month-old child at the home was unharmed, authorities said.

Deputies believe Amber Carter attempted to escape from the gunman by jumping from a second-story window, holding Mason in her arms, the statement said, but the boy did not survive his gunshot wounds.

Amber Carter had several bullet wounds, said Perry Rushing, chief of operations for the sheriff's office, and authorities believe the gunman shot her in the back as she was attempting to get out the window while holding the child. She also may have been shot again after she got outside the home, Rushing told CNN.

Amber Carter was flown to a Baton Rouge, Louisiana, hospital, and later transferred to New Orleans, Rushing said. She was in critical condition as of Sunday morning.

A neighbor in the area told deputies that he heard a gunshot and saw Carter Sr. walking to a car, a red El Camino, with a gun in his hand, the sheriff's statement said.

At 11:30 p.m., a police officer in the adjacent town of Livingston saw the vehicle entering Interstate 12 heading eastbound, the statement said. A Livingston Parish sheriff's deputy followed the car and attempted to stop it. "However, the suspect shot himself with a handgun, in plain view of the officers, as the vehicle veered off the shoulder of the interstate near the Holden exit," police said.

Records from the Livingston Parish Detention Center show that Dennis Carter Sr., of Hammond, Louisiana, had been jailed "on three separate occasions in 2009 alone, on three separate charges of violation of a protective order and one charge of aggravated assault (domestic)," the sheriff's office said.

"At this time, there do not appear to be any other suspects or victims in this ongoing investigation," police said.

Holden is about 35 miles east of Baton Rouge.