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“This bill attempts to address this big problem for the industry, the lack of financial services. But what it cannot do is get around the federal money-laundering piece of this,” said Sam Kamin, a law professor at the University of Denver who follows marijuana regulations.

Threat of federal intervention appears to be growing. American Express announced last May it would no longer handle medical marijuana-related transactions because of fear of federal prosecution. A month later, U.S. Deputy Attorney General James M. Cole gave banks an explicit directive about pot.

“Those who engage in transactions involving the proceeds of such activity may also be in violation of federal money-laundering statutes and other federal financing laws,” Mr. Cole wrote in a memo that spooked the few small banks still doing business with marijuana growers and sellers.