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Mayor Michael Bloomberg filed a formal challenge to the 2010 New York City census, saying an increase in residential vacancy rates in some neighborhoods indicated they were undercounted.

The Census Bureau should re-evaluate its tally of Bay Ridge and Bensonhurst in Brooklyn, and Astoria and Jackson Heights in Queens, Bloomberg said a letter to the bureau released today. A large number of housing units in those areas were mistakenly classified as vacant, he said.

The neighborhoods are “among the most stable, growing and vibrant” in the city, suggesting “some aspect of the census enumeration went awry,” Bloomberg said.

Census workers counted 8,175,133 people in New York City, 216,748 fewer than it estimated in 2009. The deviation is the largest of any city estimated. New York’s population could increase by “tens of thousands” if the errors are corrected, Bloomberg said.

The U.S. uses the census to allocate more than $400 billion in federal funds to cities and states each year. At least 48 other municipalities, including Washington, Miami and Dayton, Ohio, are seeking a review of their results, according to an Aug. 4 report from the Census Bureau.

The Census Bureau said the Bay Ridge and Bensonhurst areas had a vacancy rate of 10.6 percent and that it was 7.5 percent in the Astoria and Jackson Heights neighborhoods, the city said in its challenge. Those compare with 3.7 percent in the Brooklyn region and 2.9 percent in the Queens area in the 2000 census.

“What’s here is a report that just doesn’t jive with reality or the data,” Rachaele Raynoff, a spokeswoman for the Planning Department, said in a telephone interview. “It’s very important to get this right.”

The mayor is founder and majority owner of Bloomberg News parent Bloomberg LP.