The baby was born with drugs in her system and social workers were on their way to take custody of the baby.
In the video, the new father doesn't draw too much attention at first, but he tried to open a fire exit and sets off an alarm.
Hospital staffers came to see what is going on and told the suspect to leave through the main exit, not the fire exit.
At that point, it appears none of them were aware of what police say he was carrying in that plastic bag.
Glendale Police say 33-year-old Jason Bristol's baby was born at a home in Youngtown, then taken to the hospital. The baby had meth, marijuana, and morphine in her blood stream.
The police report says that Bristol wrapped the baby in blankets and put her in the plastic bag because he and the mom, "knew the child was going to be removed from them, so he wanted to get out of the hospital."
After he waited a few minutes, the exit eventually unlocked, and the suspect took the stairs to the main lobby and walked out.
When staffers at Banner Thunderbird discovered the couple and the baby were missing they got the police involved. The baby's father is now looking at a child abuse charge, and police say he was also found with a small amount of meth on him.
The baby is now in Department of Child Safety custody.