(CNN) -- Federal authorities have seen no change in the number of illegal immigration checks sought by local Arizona police and allowed under a state law partly upheld by a recent U.S. Supreme Court decision, officials said Wednesday.
In the first week after the high court upheld a portion of the controversial law, eight calls were made by Arizona law agencies inquiring into the immigration status of persons suspected of being in the United States illegally, said spokeswoman Amber Cargile of the U.S. Immigration and Customs Enforcement in Phoenix.
Those eight phone calls "resulted in the arrest of 38 aliens on immigration violations" between June 25 and July 2, Cargile said.
Comparison figures to the recent past or a year ago weren't immediately available, "but our staff reports they continue to receive what they describe as a normal volume of calls from state and local law enforcement agencies," Cargile said in an e-mail response to a CNN inquiry.
On June 25, the U.S. Supreme Court struck down key parts of the Arizona law that sought to deter illegal immigration, but let stand the controversial provision allowing police to check a person's immigration status while enforcing other laws if "reasonable suspicion" exists that the person is in the United States illegally.
Critics said that law opens the door to racial profiling.
The Phoenix Police Department and at least two sheriffs in Arizona told CNN that the law won't result in great change for their departments.
But Tucson Police Chief Roberto Villasenor expressed concern in an interview after the ruling about whether his 950-officer agency has been dealt an "impossible mandate." The state law, SB 1070, allows citizens to sue his department or others if they fail to enforce federal immigration laws, the chief said.
"Just for my agency, it will be a huge workload, just making the calls and waiting for a response on what to do," the police chief of Arizona's second-largest city said.
"I'm not sure the federal government is capable of handling all the requests that they will be receiving," Villasenor added. "I don't know what effect it will have on my agency."
At a time when the Tucson Police Department is down 160 officers because of a weakened economy, the agency now must make up to 50,000 additional phone calls a year to federal officials to verify the immigration status of persons whom officers have stopped and have reason to believe are in the country illegally, Villasenor said.
Just 70 miles from the Mexican border, the Tucson department may have to spend more than $10 million a year to book and jail up to 36,000 arrestees also suspected of being illegal immigrants, a more than 7% increase to the agency's $130 million budget, Villasenor said.