Now that the 2010 Census numbers have been released for every place in the United States, a number of local officials—including the mayors of New York and Detroit—have announced plans to file administrative challenges to counts that they contend are too low.  Based on past patterns, some lawsuits alleging undercounts also can be expected.

Census numbers indicated that New York City’s population in 2010 was 8,175,133, compared with 8,008,278 a decade earlier. That gain of about 167,000 people was smaller than expected, and city officials say it was less than the number of new housing units added over the decade. Mayor Michael Bloomberg announced the city will file a formal challenge, focusing on problems in Brooklyn and Queens.

The mayor of Detroit, Dave Bing, hopes a challenge could increase his city’s official count of 713,777 to about 750,000. As counted  by the Census Bureau, Detroit’s population fell by 25% from 2000 to 2010. Both city and regional officials say the official count could be low by tens of thousands of people.

Both cities will appeal under the Census Bureau’s Count Question Resolution program, which offers a limited opportunity to challenge the numbers. Any changes would not affect apportionment of congressional seats, counts for redistricting purposes or official census data products. The changes would be incorporated into Census Bureau population estimates, which federal agencies use as the basis for dividing program funds among the nation’s states and localities for the next decade.

Only three types of challenges are allowed. Two of them have to do with counting people in the wrong place: Localities must prove that the Census Bureau maps used the wrong boundary lines between two places or that some housing units were assigned to the wrong town. Localities also can try to prove that some housing units on the census address list were mistakenly duplicated or deleted from the count.

After the 2000 Census, according to the Census Bureau, about 2,700 residents were added to the nation’s population of 281 million. The additions were a net figure, meaning that some local totals went up by small amounts and others declined by small amounts. Most of the net additions, about 1,800, were in group quarters such as prisons, college dormitories or military barracks.

The Census Bureau also can expect some legal challenges to its 2010 count. Yesterday, the Mexican American Legal Caucus sued the state of Texas to prevent the use of 2010 Census numbers in legislative redistricting. The caucus lawsuit claims the population total from the 2010 Census “severely undercounts Latinos” and that using flawed data would violate their rights to equal representation. The suit was filed in Hidalgo County, on the Mexican border, where local officials also have argued that the 2010 Census undercounted residents in rural “colonias,” and have hired a lawyer to represent them.

Although individual cities have prevailed in some challenges, court rulings generally have given the Census Bureau wide latitude in setting procedures for conducting the census. Several notable efforts to challenge the Census Bureau counts in court have failed in recent decades. The Supreme Court rebuffed an attempt by some states to require the Census Bureau to adjust the 1990 Census to compensate for people who were missed. It also rejected a challenge by Massachusetts to the way the Census Bureau counted the overseas population in the 1990 Census. It turned down Utah’s challenge of Census Bureau counting procedures after the 2000 Census.

One issue cited by some mayors in preparing to challenge the 2010 Census counts was that census counts for their localities were markedly lower than the bureau’s most recent population estimate. New York’s estimate was 8.4 million, compared with its count of less than 8.2 million.

The population estimates, which update the census counts each year based mainly on government records, are easier for localities to challenge than the census counts. The number of jurisdictions with successful challenges to population estimates grew over the past decade,  to more than three dozen in 2008.