A 6-month-old boy is brain-dead and clinging to life after he was found with a serious head injury in his Brooklyn home this week, cops said.

The infant was taking a nap inside an apartment on Gates Avenue near Marcy Avenue in Bed-Stuy around 5:50 p.m. Tuesday when his father called 911 to report that the tot was unresponsive, and had green fluid coming out of his nose, police sources said.

The father also began performing CPR, according to the sources.

Responding EMS personnel rushed the infant to Woodhull Medical Center, cops said. He was later moved to NYU Medical Center, where he is on life support, cops said.

Both parents are being questioned in connection to the incident, and police opened a child abuse investigation on Wednesday, cops said. They are blaming each other for the child’s death, police sources said.

Cops were called to the home for one previous domestic incident report — for a dispute between the couple, police said. There were no prior child abuse incidents.

No one had been charged by Thursday afternoon.