Utah's suit challenges the method the U.S. Census Bureau used to count the population to compensate for unreturned forms.
Utah appealed after a U.S. District Court three-judge panel dismissed its case against the Census Bureau in November.
Hoping the court will rule in its favor, Utah has already completed a new plan for the 4th Congressional District the state would gain.
North Carolina's recently drawn U.S. congressional districts are contingent on the case's outcome.
Paul Murphy, director of communications for the Utah Office of the Attorney General, said the Census Bureau used hot-deck imputation procedures -- population sampling methods -- that are unconstitutional.
Murphy said that when the Census Bureau was unable to verify residency in a specific house, it counted the amount of people living next door as a means to determine a population.
He said this methodology incorrectly accounted for a number of people.
Murphy said the process, which officials used in both Utah and North Carolina, gave the latter 30,000 more people and an extra House seat.
"If you eliminate the hot-deck imputation, Utah would get the additional seat," he said.