LOS ANGELES — A key provision of a controversial Arizona immigration law upheld by the US Supreme Court this week requiring police spot-checks is "ridiculous" and could encourage crime, officials say.

The "show me your papers" policy will hurt the relationship between police and the community, discourage people from reporting crimes for fear of being targeted and be very costly, Tucson police chief Roberto Villasenor told AFP.

Provision 2(B) of Arizona's immigration law requires police to demand proof of citizenship from anyone they stop and suspect of being an illegal alien, even without probable cause.

In a victory for Obama's Republican opponents, the Supreme Court justices unanimously refused to strike down the clause Monday, saying it was unclear, before the law's actual implementation, that it raised constitutional concerns.

Justices rejected a series of other provisions, including those that would have criminalized immigrants for failing to register with the federal government, or for seeking work or working without proper documents.

They also struck down a clause that would have allowed police to arrest without a warrant those suspected of being eligible for deportation.

"This is bad law," said Villasenor, stressing that local police should not fulfill the role of federal immigration agents.

"Our mandate is the protection of lives and properties of everyone who lives in our communities, regardless of their immigration status."

The police chief acknowledged that Arizona may have put forth its law out of frustration with the federal government's struggles at enforcing the nation's immigration laws in a country with some 11.5 million illegal immigrants.

But he said local law enforcement should not take up that burden, and warned of "more crime" ahead now that the Supreme Court has approved the police checks.

"It will hinder communication between us and segments of our community, because if they're not talking to us, if they're not reporting things to us, then there's no fear or deterrent on the part of criminals," Villasenor said.

"That's a severe problem for us on how we conduct our jobs."

A large chunk of Tucson's population of half a million people -- 41.6 percent -- is Latino.

Utah and four other states have approved a package of laws similar to the one in Arizona, which had been suspended by a judge pending the Supreme Court's decision but which the state has now begun to implement.

Chris Burbank, the police chief in Utah's capital Salt Lake City, also expressed fears of a climate of impunity if the state follows Arizona's lead.

"Even if we go with a conservative estimate, potentially a quarter of our population is going to mistrust the police," said Burbank. About 30 percent of Utah's population is Hispanic.

"When the public doesn't communicate with the police, that's when criminal activity thrives," he added. "Because criminals know that people are not going to report them."

Rights groups around the country have condemned the authorization to detain people based on "reasonable suspicion" that they are undocumented, warning it could lead to racist bias.

They say that law enforcement agents are likely to rely on suspects' clothing, skin color and accent to determine whether they are undocumented.

"How can we expect officers to investigate a crime which centers around national origin and we then tell them they're not allowed to consider national origin?" Villasenor said.

"That is the ridiculous nature that this law has gone to."

But Sheriff Joe Arpaio of Arizona's Maricopa County, who calls himself "America's toughest sheriff," hailed the Supreme Court ruling as a victory because "it changes nothing."

"We are going to continue doing what we have being doing. We'd been enforcing that element anyway," he told CBS5 television.

Arpaio is at the center of a years-old criminal probe by the Justice Department, which also launched a civil rights suit against him in May for violating the rights of Latinos.

Critics of the Arizona law say it comes at a significant cost to the state. In Tucson, some 36,000 people are arrested each year on suspicion of being illegal immigrants, according to Villasenor.

However, he noted, if authorities now need to check the immigration status of all of those suspects, his office will spend more than $10 million each year to detain suspects while they are verifying their information.

That hefty figure does not take into account the mountains of paperwork or the cost of fending off the numerous claims of discrimination that police are likely to face in the courts.