The question on the minds of Arizona immigrants Tuesday was how law enforcement agencies will enforce the state's "show your papers" policy now that the U.S. Supreme Court has ruled it constitutional.

The high court struck down on Monday the other three elements of Arizona's controversial SB 1070 immigration law, but left standing the provision requiring police to verify the immigration status of suspected undocumented migrants stopped in the course of enforcing other laws.

The show your papers provision was blocked by a federal district court in 2010 pending a final judicial determination on the U.S. Justice Department's lawsuit challenging the Arizona measure.

Yet even after the Supreme Court's ruling, many Arizona police departments remain uncertain over exactly how to proceed.

Tucson's police chief, Roberto Villaseñor, told Efe the department is consulting with attorneys on the Supreme Court's decision, though he stressed that enforcing the law represents a new challenge for a force struggling with limited resources.

"Previously, the police had the discretion to call immigration during a traffic stop. If there were other more urgent calls, such as a robbery, a rape, the officer gave priority to the needs of the community. Now this law takes this option away from us," he said.

Pima County Sheriff Clarence Dupnik, whose jurisdiction includes Tucson, said his deputies are trained to look for suspicious behavior, not to enforce federal immigration law.

An outspoken critic of SB 1070, the sheriff acknowledged that Arizona law enforcement agencies will be under intensified public scrutiny as they apply the show your papers policy.

Under the terms of the law, police and sheriff's departments face potential lawsuits, not only for racial profiling by people who feel they were unfairly singled out, but also for insufficient zeal in enforcing show your papers.

"It's a terrible situation for any police department," Dupnik told Efe.

Here in Phoenix, police chief Daniel V. Garcia has sought to reassure the Hispanic community with a pledge that his department will not engage in racial profiling.

"All people will be treated with respect and dignity," he said after the Supreme Court ruling.

A community forum on the implications of SB 1070 attracted a number of immigrants, including Juan Gonzalez, an undocumented Mexican national who has lived in Arizona for 12 years.

"I had the hope the Supreme Court would completely eliminate SB 1070, but they left alive what I believe is its worst part," he said, adding that sympathetic activists have advised immigrants to know their rights, say nothing if stopped by police and refrain from driving without a license.

"I think that is the hardest," Garcia said. "I depend on my car to be able to go to work. That (not driving) will be impossible, so I will be at risk all the time."

Another immigrant, Maria Ramirez, said that from now on she "will look at police differently."

"They can tell us there won't be violations of civil rights, but I can't avoid feeling a lot of mistrust and fear," she said. EFE