Two separate investigations are now under way into the death of a 5-year-old Brooklyn boy who fell 100 feet down an elevator shaft in his Williamsburg apartment building Tuesday morning.

Yesterday, the Brooklyn district attorney’s office announced it had launched an investigation into how Jacob Neuman fell more than 100 feet to his death in an elevator shaft while on his way to school with his 8-year-old brother. The elevator car was stuck between the 10th and 11th floors and when the door of the elevator opened, the boy jumped onto the 10th-floor landing, lost his footing, and fell down the shaft.

A spokesman for the Brooklyn district attorney, Jerry Schmetterer, said the office is “going to be asking for the records that pertain to the case.” Mr. Schmetterer said that as part of the investigation, the attorney’s office would be probing the New York City Housing Authority, the building’s landlord.

The New York City Housing Authority, which has oversight responsibility for the building, said in a statement yesterday that it has launched its own investigation.

Council Member David Yassky, whose district includes the building, in a letter yesterday to the housing authority chairman, Tino Hernandez, is calling for a full internal audit of all housing authority elevators.

Manhattan’s president, Scott Stringer, described the accident as a “wake-up call for the New York City Housing Authority,” adding that in the current fiscal year, the authority has an operating budget deficit of $195 million. The accident is also raising questions about the impact federal funding cuts have had on the safety of public housing. More than half of the housing authority’s operating budget comes from federal funds, and in the last seven years it has lost a total of $611 million in federal dollars. The operating budget for the 2008 fiscal year is $2.8 billion.

According to a spokesman for the housing authority, Howard Marder, the elevator, which was installed in 1970, was slated to be completely replaced in 2004, at a cost of $3.4 million. “Because of federal budget cuts to the capital budget, that was postponed to 2009,” Mr. Marder said in an interview yesterday.

Residents at the building, at 30 Clymer St. in Williamsburg, Brooklyn, have said the elevator was a constant source of problems.

It is the responsibility of the housing authority to inspect elevators five times every two years in buildings it controls. The building in the Taylor-Wythe apartment complex houses, where Tuesday’s accident took place, had been deemed “unsatisfactory” by the housing authority in at least 17 of the 21 inspections between 2004 and 2007, records on the Department of Building’s Web site show.

Mr. Marder said that an elevator could be deemed “unsatisfactory” for relatively minor problems, such as if a lightbulb had gone out or if the elevator car was dirty. For more serious problems, Mr. Marder said, the Department of Buildings would have issued a violation, which hadn’t happened in this case.

In a letter yesterday to Mayor Bloomberg, Gregory Floyd, the president of Teamsters Local 237, which represents housing authority employees, said: “Even if NYCHA was properly funded, this accident may have occurred, but the incident serves as an appalling example of the federal government’s failure to meet its obligation to fund federal housing.”

A spokesman for the Department of Buildings was unable to say by press time yesterday if the department kept a record of injuries and deaths sustained in elevators in New York. However, a search of newspaper reports shows that at least seven people have died after falling down elevator shafts since 2004.