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Fire officials told ABC11's sister station KTRK the baby was initially dropped off at a nearby church.
According to HFD District Chief Steve Dunbar, HFD Station 63 got a knock on the door around 4:40 a.m.
When firefighters answered, they found a man had the baby in his arms.
He told crews he was from the church and then handed them the boy, who appears to be full term.
The umbilical cord was still attached to the baby. He was transported to Northeast Memorial Hermann Hospital.
The man who dropped him off did not leave an ID or his name.
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Houston police are now trying to find the baby's parents.
Due to the child's age, the drop off appears to fall under the Baby Moses law, also known as the Safe Haven law.
It only applies to babies 60 days old or younger who are unharmed and safe.
The law allows parents to take their baby to any hospital, fire station, or EMS station in Texas.
Other Texas news: Man intentionally rams pickup truck into Dallas TV station building