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(CNN) -- Utility companies will return Sunday to restore power in parts of Rayne, Louisiana, after a tornado pummelled the region, killing at least one person.
A Louisiana mother who died sheltering her child during the tornado was identified early Sunday as Jalisa Granger, a sheriff's office official said.
The 21-year-old's body was found by "a family member who lived nearby" who went to check on her, said Maxine Trahan, a spokeswoman for the Acadia Parish Sheriff's Office in Rayne, Louisiana, adding that the "child was OK."
Granger was killed when a tree fell on her house in the storm.
Eleven people were injured, she said.
"There's a lot of damage out there," Trahan said. "Most residents were evacuated, leaving for other relatives' homes. About 20 (who were) evacuated didn't have somewhere to go, but were taken to the local fire department."
Utility companies will be returning to the area Sunday morning to help restore power, she said.
The storm that killed Granger was one of at least two twisters tied to a weather system that has caused major damage in the state and wreaked havoc on Mardi Gras festivities.
The National Weather Service confirmed that tornadoes hit the city of Rayne, about 80 miles west of Baton Rouge, and the nearby city of Crowley on Saturday morning.
Packing winds between 111 and 135 mph, the tornado was 300 yards wide and produced damage over a 5-mile stretch, according to the weather service.
The northwest section of Rayne was especially hard hit, with video from CNN affiliate KATC showing several buildings leveled, lots reduced to rubble and large trees knocked down.
Petijean said the city's electricity infrastructure was badly damaged, with power going out for all its 10,000 residents soon after the tornado came through.
In addition, several houses were knocked off their foundations and there were reports of gas leaks, which led to mandatory evacuations of about 1,500 residents in the city's northwest, Petijean said.
The mayor said a curfew was imposed in part of the city, with people asked to stay indoors until 6 a.m. Sunday while authorities check to ensure all is safe. Some of those evacuated are being cared for by the Red Cross.
The impact zone is an area about one to two square miles, said Rayne police dispatcher Whitney Thibodaux. Among the buildings affected were a public housing units and Rayne High School, with damage to the computer room, library and gym.
Three people, meanwhile, suffered injuries when the twister hit Crowley, according to the National Weather Service.
Debris was reported along a 2-mile-long damage path on Interstate 10, and there was damage to a Waffle House, car wash and several residences.
About 150 miles to the east, meanwhile, revelers and residents of New Orleans were soaked much of Saturday as steady rains fell on the city. This weekend -- the last one before Ash Wednesday -- is traditionally one of the busiest in The Big Easy, with people partying and enjoying Mardi Gras festivities.
The weather forced several changes to the Mardi Gras schedule, including the delay of the Krewe of Endymion parade from Saturday to Sunday, according to a release from the New Orleans Police Department. Other parade-related festivities were pushed up to start earlier Saturday, given the rain-soaked forecast for Saturday afternoon and beyond.
The rain stopped later Saturday in New Orleans and the weather service's forecast called for sunny conditions Sunday, with high temperatures in the lower 60s.
A flood advisory remains in effect through Monday morning for numerous communities along the Mississippi River, including parts of Chicot and Desha counties in Arkansas; Adams, Bolivar, Isaquena, Washington, Madison and Wilkinson counties in Mississippi; and Claiborne, East Caroll, Jefferson, Tensas and Warren parishes in Louisiana.
There were also flood warnings in effect for the Atchafalaya River at Morgan City, Louisiana, through Sunday afternoon; the Tchefuncte River in Covington, Louisiana, through Monday at noon; and the Bogue Falaya River at Camp Covington, Louisiana, through Tuesday morning.
CNN's Rick Martin, Craig Bell, Tina Burnside and Jacqui Jeras contributed to this report.