Foreign workers should always carry their visa and passport, their I-797 approval form, as well as their I-94 arrival-departure record, said Wildes.

The practical advice for work visa holders as a result of this decision is to carry documentation, said Marko Maglich, an immigration attorney at White & Case in New York. If an H-1B worker hasn't been in the habit of carrying their documents, he or she "better do it now," he said.

It's uncertain how this law will play out in the state over the long term.

If an H-1B worker carries a California drivers license and is pulled over on a traffic stop in Arizona, the presumption of legal status with an Arizona driver's license goes away, said Jorge Lopez, co-chair of the Immigration & Global Migration Practice at Littler Mendelson.

Lopez advises that visa holders at least carry copies of all their pertinent documents.