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(CNN) -- Arizona's Legislature has passed a controversial bill that would allow business owners, as long as they assert their religious beliefs, to deny service to gay and lesbian customers.

The bill, which the state House of Representatives passed by a 33-27 vote Thursday, now goes to Gov. Jan Brewer, a Republican and onetime small business owner who vetoed similar legislation last year but has expressed the right of business owners to deny service.

"I think anybody that owns a business can choose who they work with or who they don't work with," Brewer told CNN in Washington on Friday. "But I don't know that it needs to be statutory. In my life and in my businesses, if I don't want to do business or if I don't want to deal with a particular company or person or whatever, I'm not interested. That's America. That's freedom."

As expected, the measure has drawn criticism from Democrats and business groups who said it would sanction discrimination and open the state to the risk of damaging litigation.

On Friday, the LGBT group Wingspan staged a protest march to the governor's office that drew about 200 people. Some carried signs with messages "God created us all equal" and "Shame on Arizona."

Tucson-based Rocco's Little Chicago Pizzeria posted a photo on its Facebook page of a sign with a message for state lawmakers: "We reserve the right to refuse service to Arizona legislators."

"It's a ridiculous bill," pizzeria manager Evan Stevens told CNN on Friday. "Arizona has much bigger problems than allowing businesses to discriminate against people."

In a statement, Anna Tovar, the state senate Democratic minority leader, said: "With the express consent of Republicans in this Legislature, many Arizonans will find themselves members of a separate and unequal class under this law because of their sexual orientation. This bill may also open the door to discriminate based on race, familial status, religion, sex, national origin, age or disability."