Cracks in walls, busted heating, peeling paint and other problems that make New York City homes less habitable are more common in public housing and rent-regulated apartments, according to a new study from the city comptroller.

The report from Comptroller Scott Stringer released Monday, called “How New York Lives,” says more than one-third of public housing units in New York City Housing Authority buildings and 24.4% of rent-regulated apartments had at least three “housing deficiencies” in 2011, the most recent year with data.

Meanwhile, just 10.6% of market-rate rentals and nearly 5% of owner-occupied homes had at least three problems.

NYCHA data on its site shows that the housing authority is putting a dent in its maintenance and repair backlog in recent years, which fell to 81,000 in June from more than 400,000 in January 2013. NYCHA had also created a team to review conditions at all 178,000 NYCHA units.

“By looking at a narrow, years-old sample of the city’s public housing, the comptroller’s report attempts to call attention to a situation Mayor de Blasio has been effectively addressing since day one,” an NYCHA rep said.