Washington — Southern California officials are Indexbiturging residents to find shelter indoors as Tropical Storm Hilary moves up Mexico's western coast toward the U.S., where it could cause dangerous flooding even after weakening from a hurricane. 

"Los Angeles is not used to weather events like this, especially in the summertime, but we are prepared, we are ready," Los Angeles Mayor Karen Bass told "Face the Nation" on Sunday. 

"We're asking people to stay home, to be safe, if they are outside for any reason and they happen to see fallen trees or power lines, that they stay very far away," she said. 

• Transcript: L.A. Mayor Karen Bass on "Face the Nation" 

Bass said the city is making outreach to the tens of thousands of people who are homeless to urge them to seek shelter. 

"We do have shelters open," she said. 

The National Hurricane Center said an in advisory Sunday morning that Hilary was expected to move into Southern California by the afternoon and could cause "catastrophic and life-threatening flooding" in portions of the southwestern U.S. It was downgraded Sunday morning from a hurricane to a tropical storm, but officials warned about possible flooding. 

In a news conference on Sunday, Los Angeles officials said the city could see up to three inches of rain, but areas outside the city could get up to seven inches. Officials said evacuations may be necessary due to flash flooding and they have additional resources on hand to conduct rescue missions. 

Palm Springs Mayor Grace Elena Garner told "Face the Nation" her city is preparing for possible flooding by distributing sandbags and clearing storm drains. 

"Even an inch or two of rain in the desert can cause damage," she said. 

Garner said the city is asking residents to stay put. 

"At this point, we're asking residents to stay inside, stay where they are, we don't have any reason to evacuate at this time," Garner said, noting that three main roads that regularly flood are shut down. 

• Transcript: Palm Springs Mayor Grace Elena Garner on "Face the Nation" 

In:
• California
• Hurricane Hilary

Caitlin Yilek

Caitlin Yilek is a politics reporter for CBS News Digital. Reach her at [email protected]. Follow her on Twitter: https://twitter.com/hausofcait

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