The NYPD does a good job alerting the city’s housing authority about dangerous criminal residents — but NYCHA routinely does little or nothing with the information, according to a new Department of Investigation report released Tuesday.

The follow-up DOI report comes after a 2015 investigation that found that violent criminals living in public-housing were getting pass because the NYPD rarely alerted housing officials of their offenses – and when the department did, the Housing Authority seldom moved to evict.

The new report said that although the NYPD’s communication with NYCHA has “improved significantly” the Housing Authority is still failing to enforce its policies by removing the criminals, which include violent felons, drug traffickers and gang members.

“NYCHA has an obligation to protect the residents of its buildings. Its failure to do so, even after DOI’s Report in 2015, is inexcusable,” DOI Commissioner Mark Peters said. “Unlike other concerns at NYCHA, this is not the result of underfunding or lack of tools. Rather it is a repeated failure to act decisively long after a problem and solution have been well documented.”

The 2015 report found that neither the cops nor NYCHA were living up to the terms of a 1996 agreement requiring them to act when a tenant was nabbed in order to keep non-law breaking residents of NYCHA’s 328 public housing complexes safe.

According to NYPD stats for 2016, 14 percent of murders, 19 percent of shootings, and 13 percent of rapes were committed on NYCHA premises.

The follow-up report into the matter found that the NYPD has made improvement in reporting most on-site arrests of public housing tenants.

In 2016, the NYPD increased its reporting of arrests made on NYCHA property by 79 percent, but the department was lacking in informing housing officials of arrests made of tenants off NYCHA grounds, the report found.

A police source told The Post that it should be NYCHA’s responsibility to keep tabs of residents who commit crimes off-site.

“If they’re arrested off NYCHA property, there’s no procedure by the (police) department for us to notify anybody. So I don’t understand why they’re throwing any shots our way when there’s no procedure in place,” said the source.

The source added, “We should enforce the laws, but we shouldn’t have keep track of their residents.”

NYCHA is failing to seek evictions of known criminal tenants with arrests of involving shootings, narcotics, and gang-related activities, according to the new report.

The agency “overlooks even blatant and repeated violations” of the permanent exclusion policy, according to the report.

In 2016, the Housing Authority settled 32 percent of tenant termination cases based on criminal activity, but brought only 1 percent of cases to a hearing for possible eviction, the report said.

The report recommends 10 steps the agencies should take to correct the issues that includes NYCHA’s Law Department to more aggressively prosecute tenancy termination cases.

In response to the report, the Housing Authority issued a statement saying, “NYCHA works closely in partnership with the NYPD to ensure public housing residents have safe, stable homes.”

“Many of the Department of Investigation’s recommendations highlight the progress we’ve made in improving communication between our agencies. We will continue our work with NYPD and DOI to remove threats from developments and support the public safety of New Yorkers,” the statement continued.

The NYPD said in a statement, “The Department continues to work with NYCHA to ensure the safety of all its residents. We will respond formally to DOI’s report in the coming weeks.”