Brown issued a veto Sunday, saying "enabling illegal and destructive drug use will never work."
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VIDEO: Here's what a safe injection site could look like in SF
VIDEO: Here's what a safe injection site could look like in San Francisco
San Francisco could still choose to open such a site but it would be in violation of federal and state law.
Advocates of "safe injection" sites say the supervised locations prevent drug overdoses and provide access to counseling.
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RELATED: Safe injection sites remain hot debate in San Francisco
The U.S. government and other critics say taxpayers shouldn't be enabling users.
San Francisco Mayor London Breed has vowed to open a supervised injection site in the city, where public drug use is a major problem. She vowed to continue to work toward a solution and move the effort forward.
There are safe injection sites in other countries, but none in the United States.