“They are focusing on one particular group of people, Hispanics, and here along the border … it can be pretty challenging to determine who’s here legally and who isn’t,” said Estrada, the sheriff of Santa Cruz County, which flanks Mexico in southern Arizona.

He is among police chiefs throughout the state grappling with the practical aspects of just how to implement the law in a state where there are about two million Hispanics – nearly a third of the state’s 6.5 million people – most of whom are there legally. There were an estimated 360,000 unauthorized immigrants in Arizona as of January 2011, according to government figures.

The provision requires police to make a reasonable attempt to check the immigration status of people they stop, even for an offense such as jay walking, if they suspect that they are an illegal immigrant.