The household estimation method is used as a last resort when census workers repeatedly fail to find anyone home.
When census workers were unable to count people in a household despite repeated visits, the Census Bureau assumed through statistical "imputation" that the same number of people lived there as in a neighboring dwelling.
The court will hear an appeal from Utah, which claims that methods used in the 2000 census robbed the state of one of its congressional seats. The court also wants both sides to give their views on whether the Supreme Court has jurisdiction over the case.
If the justices conclude that they do not have jurisdiction, the decision of a lower court against Utah would stand.
In the 2000 census, imputation accounted for less than half a percent of the total U.S. population. If it had not been used, Utah would have one more seat in the House and North Carolina would have one fewer.
The court is expected to hear the case next fall, and its ruling would not affect races to fill congressional seats in the November election.
Utah lost a separate census challenge last year, when the high court refused to hear complaints that the census wrongly excluded Mormon missionaries working overseas.
In the latest Utah case, a panel of three federal judges voted 2-1 in November to dismiss the state's lawsuit challenging the household estimation technique.
The lower court said it is reasonable to assume that households in the same neighborhood will be of similar size.
In its appeal to the Supreme Court, the state argued that the phrase "actual enumeration" means the Constitution's framers specifically ruled out guesswork.
"There simply is no plausible understanding of the term" that would permit the use of estimated numbers in apportioning House seats, lawyers for the state wrote.
Utah Attorney General Mark Shurtleff has said the estimation method disproportionately benefited North Carolina, which picked up a seat in Congress after the head count.
The state also argued the estimation method is little different than another statistical tool called "sampling." The Supreme Court split 5-4 along ideological lines to rule in 1999 that sampled census numbers cannot be used to parcel out congressional seats.
The 435 House seats are redistributed according to state population after each decennial census.
At the time, the Census Bureau and the Democratic Clinton administration said sampling would help make up for an expected undercount of minorities in the 2000 head count. Democrats generally support the practice while Republicans oppose it.
In the current case, the Republican Bush administration defended use of the household estimation technique, and urged the Supree Court to uphold the lower court.
In the formula used to determine House seats, Utah finished just 857 residents behind North Carolina, another fast-growing state. The figures gave North Carolina its 13th seat and left Utah with three.
Utah has fought its loss through several courts, and hoped the Supreme Court would accept its appeal as part of the current term. That would have meant a ruling by July, in time to affect the fall elections.
The court apparently did not see the same urgency. Results of the congressional reapportionment are already set, which may lead the court to conclude there is nothing to be settled by continuing with the case.
The Supreme Court affirmed another lower court ruling against Utah in November. In that case, Utah claimed that it was unfair to count federal workers and military personnel posted overseas while excluding others temporarily living outside the United States.
North Carolina Attorney General Roy Cooper intervened in both lawsuits in defense of the census results.
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