A 6-week-old baby girl died on Thursday morning after falling eight stories down an elevator shaft in Brooklyn, police said.

Her mother was on the 23rd floor of 3415 Neptune Ave. in Coney Island when the elevator doors opened around 10:20 a.m. 

Not realizing the elevator had not arrived, the mother and her baby fell into the shaft and landed on the top of the out-of-service elevator on the 15th floor, police said.

The infant, identified as Areej Ali, was taken to Coney Island Hospital, where she was pronounced dead, police said.

The building had 50 open Department of Buildings violations, according to city records.

This particular elevator was last inspected on Aug. 8 and a nonhazardous violation was issued because the phone in it didn’t work, a DOB official said. The elevator was not shut down at the time.

It last passed a thorough inspection in January with a load test in which weights are rolled into the car to make sure it can hold its capacity. These inspections are held once every five years, the official said.

“Our inspectors will remain on scene to conduct a full investigation into this tragic accident,” a DOB spokesman said in an email. “We will be testing all of the elevators in the complex to ensure they are operating safely.”

A cease-use order was issued until the investigation is completed.

(With Alison Fox)