It is not clear whether the burns were suffered by accident. The 23-year-old mother was taken into custody for questioning.
She lives at 445 15th Avenue with her two children and a teenager, police said.
Authorities said she claimed she was giving the baby a bath and the water was too hot, which is how the kid was burned.
Police were still investigating. She has not been charged.
The 8-month-old baby was in critical condition at St. Barnabas Medical Center.
The mother was released to go to the hospital to see her baby, police said.
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