The bill is in response to the Bay Area Rapid Transit Agency's shut down of wireless services two years ago during a protest.
Current law requires a court order before telephone services are cut. Democratic Senator Alex Padilla, the bill's author, says wireless service should have the same protections.
The Governor's veto message said law enforcement should have the ability to shut down service during an emergency.
Padilla says his bill will address that concern.
PADILLA: "We'll continue to work to strike the right balance of what's reasonable for law enforcement personnel to maintain our safety but at the same time require the proper transparency and judicial approvals for what's really an extreme act, the shutting down the ability of people to communicate."
Padilla says cutting off wireless service creates public safety concerns because people can't call 9-1-1.